Commit 7837a0cd authored by Michael Wagner's avatar Michael Wagner
Browse files

added 150 OEIS dump for Frederik

parent 495ee85e
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<computation><program><author>_John Cannon_</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>Dec 23 2006</date><source_code> D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [1..1000] ]; // _John Cannon_, Dec 23 2006
</source_code></program><program><author>_Muniru A Asiru_</author><language_tag>(GAP)</language_tag><file_ending>.gap</file_ending><date>Oct 15 2017</date><source_code> A000001 := Concatenation([0], List([1..500], n -&gt; NumberSmallGroups(n))); # _Muniru A Asiru_, Oct 15 2017
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> my(a=[1,2,2]); for(n=3,80, for(i=1,a[n],a=concat(a,2-n%2))); a
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> {a(n) = local(an=[1, 2, 2], m=3); if( n&lt;1, 0, while( #an &lt; n, an = concat( an, vector(an[m], i, 2-m%2)); m++); an[n])};
</source_code></program><program><author>_John Tromp_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Apr 09 2011</date><source_code> a = 1:2: drop 2 (concat . zipWith replicate a . cycle $ [1,2]) -- _John Tromp_, Apr 09 2011
</source_code></program><program><author>_David Eppstein_</author><language_tag>(Python)</language_tag><file_ending>.py</file_ending><date>Oct 15 2016</date><source_code>
# For explanation see link.
def Kolakoski():
x = y = -1
while True:
yield [2,1][x&amp;1]
f = y &amp;~ (y+1)
x ^= f
y = (y+1) | (f &amp; (x&gt;&gt;1))
K = Kolakoski()
print([next(K) for _ in range(100)]) # _David Eppstein_, Oct 15 2016
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> O1 := MaximalOrder(QuadraticField(D)); _,f := IsSquare(D div Discriminant(O1)); ClassNumber(sub&lt;O1|f&gt;);
</source_code></program><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Jul 16 1999</date><source_code> {a(n) = qfbclassno(-4*n)}; /* _Michael Somos_, Jul 16 1999 */
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [ 0 : n in [0..100]];
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> vector(100,n,0)
</source_code></program><program><author>unknown</author><language_tag>(R)</language_tag><file_ending>.r</file_ending><date>unknown</date><source_code> rep(0,100)
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>May 07 2012</date><source_code>
a000004 = const 0
a000004_list = repeat 0 -- _Reinhard Zumkeller_, May 07 2012
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Apr 27 2003</date><source_code> {a(n) = if( n==0, 0, numdiv(n))}; /* _Michael Somos_, Apr 27 2003 */
</source_code></program><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Apr 27 2003</date><source_code> {a(n) = n=abs(n); if( n&lt;1, 0, direuler( p=2, n, 1 / (1 - X)^2)[n])}; /* _Michael Somos_, Apr 27 2003 */
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> {a(n)=polcoeff(sum(m=1, n+1, sumdiv(m, d, (-log(1-x^(m/d) +x*O(x^n) ))^d/d!)), n)} \\ _Paul D. Hanna_, Aug 21 2014
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [ NumberOfDivisors(n) : n in [1..100] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
</source_code></program><program><author>_Zerinvary Lajos_</author><language_tag>(MuPAD)</language_tag><file_ending>.MNB</file_ending><date>May 13 2008</date><source_code> numlib::tau (n)$ n=1..90 // _Zerinvary Lajos_, May 13 2008
</source_code></program><program><author>_Zerinvary Lajos_</author><language_tag>(Sage)</language_tag><file_ending>.sage</file_ending><date>Jun 04 2009</date><source_code> [sigma(n, 0) for n in range(1, 105)] # _Zerinvary Lajos_, Jun 04 2009
</source_code></program><program><author>_James Spahlinger_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Oct 07 2012</date><source_code>
divisors 1 = [1]
divisors n = (1:filter ((==0) . rem n)
[2..n `div` 2]) ++ [n]
a = length . divisors
-- _James Spahlinger_, Oct 07 2012
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Jul 12 2013</date><source_code>
a000005 = product . map (+ 1) . a124010_row -- _Reinhard Zumkeller_, Jul 12 2013
</source_code></program><program><author>_Stefano Spezia_</author><language_tag>(Python)</language_tag><file_ending>.py</file_ending><date>Nov 05 2018</date><source_code>
from sympy import divisor_count
for n in range(1, 20): print(divisor_count(n), end=', ') # _Stefano Spezia_, Nov 05 2018
</source_code></program><program><author>_Muniru A Asiru_</author><language_tag>(GAP)</language_tag><file_ending>.gap</file_ending><date>Mar 05 2019</date><source_code> List([1..150],n-&gt;Tau(n)); # _Muniru A Asiru_, Mar 05 2019
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> (a(n)=sqrtint(prime(n))); vector(100,n,a(n)) \\ Edited by _M. F. Hasler_, Oct 19 2018
</source_code></program><program><author>_Charles R Greathouse IV_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Apr 26 2012</date><source_code> apply(sqrtint,primes(100)) \\ _Charles R Greathouse IV_, Apr 26 2012
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> apply( A000006=n-&gt;sqrtint(prime(n)), [1..100]) \\ _M. F. Hasler_, Oct 19 2018
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Mar 24 2012</date><source_code> a000006 = a000196 . a000040 -- _Reinhard Zumkeller_, Mar 24 2012
</source_code></program><program><author>_Albert Lahat_</author><language_tag>(Python)</language_tag><file_ending>.py</file_ending><date>Jun 25 2020</date><source_code>
from sympy import sieve
A000006 = lambda n: int(sieve[n]**.5)
print([A000006(n) for n in range(1,100+1)])
# _Albert Lahat_, Jun 25 2020
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> {a(n) = !n};
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [1] cat [0:n in [1..100]]; // Sergei Haller, Dec 21 2006
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>May 07 2012</date><source_code>
a000007 = (0 ^)
a000007_list = 1 : repeat 0
-- _Reinhard Zumkeller_, May 07 2012, Mar 27 2012
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Apr 01 2003</date><source_code> {a(n) = if( n&lt;-17, -a(-18-n), if( n&lt;0, 0, polcoeff( 1 / ((1 - x) * (1 - x^2) * (1 - x^5) * (1 - x^10)) + x * O(x^n), n)))}; /* _Michael Somos_, Apr 01 2003 */
</source_code></program><program><author>_Joerg Arndt_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Oct 02 2013</date><source_code> Vec( 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)) + O(x^66) ) \\ _Joerg Arndt_, Oct 02 2013
</source_code></program><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Mar 06 2018</date><source_code> {a(n) = my(r = (n-1)%10 + 1); (n^3 + 27*n^2 + (191 + 3*[4, 13, 0, 5, 8, 9, 8, 5, 0, 13][r])*n + 25)\600 + 1}; /* _Michael Somos_, Mar 06 2018 */
</source_code></program><program><author>_Tani Akinari_</author><language_tag>(Maxima)</language_tag><file_ending>.lisp</file_ending><date>Jun 21 2013</date><source_code> a(n):=floor(((n+17)*(2*n^2+20*n+81)+15*(n+1)*(-1)^n+120*((floor(n/5)+1)*((1+(-1)^mod(n,5))/2-floor(((mod(n,5))^2)/8))))/1200); /* _Tani Akinari_, Jun 21 2013 */
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Dec 15 2013</date><source_code>
a000008 = p [1,2,5,10] where
p _ 0 = 1
p [] _ = 0
p ks'@(k:ks) m = if m &lt; k then 0 else p ks' (m - k) + p ks m
-- _Reinhard Zumkeller_, Dec 15 2013
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [#RestrictedPartitions(n,{1,2,5,10}):n in [0..60]]; // _Marius A. Burtea_, May 07 2019
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Nov 17 1999</date><source_code> {a(n) = if( n&lt;0, 0, polcoeff( prod( k=1, n, 1 + x^k, 1 + x * O(x^n)), n))}; /* _Michael Somos_, Nov 17 1999 */
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> {a(n) = my(A); if( n&lt;0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) / eta(x + A), n))};
</source_code></program><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Aug 13 2017</date><source_code> {a(n) = my(c); forpart(p=n, if( n&lt;1 || p[1]&lt;2, c++; for(i=1, #p-1, if( p[i+1] &gt; p[i]+1, c--; break)))); c}; /* _Michael Somos_, Aug 13 2017 */
</source_code></program><program><author>_Altug Alkan_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Mar 20 2018</date><source_code> lista(nn) = {q='q+O('q^nn); Vec(eta(q^2)/eta(q))} \\ _Altug Alkan_, Mar 20 2018
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> Coefficients(&amp;*[1+x^m:m in [1..100]])[1..100] where x is PolynomialRing(Integers()).1; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Sep 09 2015</date><source_code>
import Data.MemoCombinators (memo2, integral)
a000009 n = a000009_list !! n
a000009_list = map (pM 1) [0..] where
pM = memo2 integral integral p
p _ 0 = 1
p k m | m &lt; k = 0
| otherwise = pM (k + 1) (m - k) + pM (k + 1) m
-- _Reinhard Zumkeller_, Sep 09 2015, Nov 05 2013
</source_code></program><program><author>_Emanuele Munarini_</author><language_tag>(Maxima)</language_tag><file_ending>.lisp</file_ending><date>Feb 24 2014</date><source_code> num_distinct_partitions(60,list); /* _Emanuele Munarini_, Feb 24 2014 */
</source_code></program><program><author>_Vladimir Kruchinin_</author><language_tag>(Maxima)</language_tag><file_ending>.lisp</file_ending><date>Sep 07 2014</date><source_code>
h(n):=if oddp(n)=true then 1 else 0;
S(n,m):=if n=0 then 1 else if n&lt;m then 0 else if n=m then h(n) else sum(h(k)*S(n-k,k),k,m,n/2)+h(n);
makelist(S(n,1),n,0,27); /* _Vladimir Kruchinin_, Sep 07 2014 */
</source_code></program><program><author>_Peter Luschny_</author><language_tag>(SageMath)</language_tag><file_ending>.sage</file_ending><date>Nov 11 2020</date><source_code> # uses[EulerTransform from A166861]
a = BinaryRecurrenceSequence(0, 1)
b = EulerTransform(a)
print([b(n) for n in range(56)]) # _Peter Luschny_, Nov 11 2020
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(Axiom)</language_tag><file_ending>.unknown</file_ending><date>unknown</date><source_code> [eulerPhi(n) for n in 1..100]
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [ EulerPhi(n) : n in [1..100] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
</source_code></program><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Feb 05 2011</date><source_code> {a(n) = if( n==0, 0, eulerphi(n))}; /* _Michael Somos_, Feb 05 2011 */
</source_code></program><program><author>unknown</author><language_tag>(Sage)</language_tag><file_ending>.sage</file_ending><date>unknown</date><source_code>
# euler_phi is a standard function in Sage.
def A000010(n): return euler_phi(n)
def A000010_list(n): return [ euler_phi(i) for i in range(1,n+1)]
# Jaap Spies, Jan 07 2007
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> { for (n=1, 100000, write("b000010.txt", n, " ", eulerphi(n))); } \\ _Harry J. Smith_, Apr 26 2009
</source_code></program><program><author>_Zerinvary Lajos_</author><language_tag>(Sage)</language_tag><file_ending>.sage</file_ending><date>Jun 06 2009</date><source_code> [euler_phi(n) for n in range(1, 70)] # _Zerinvary Lajos_, Jun 06 2009
</source_code></program><program><author>_Emanuele Munarini_</author><language_tag>(Maxima)</language_tag><file_ending>.lisp</file_ending><date>Mar 26 2011</date><source_code> makelist(totient(n),n,0,1000); /* _Emanuele Munarini_, Mar 26 2011 */
</source_code></program><program><author>unknown</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>unknown</date><source_code> a n = length (filter (==1) (map (gcd n) [1..n])) -- _Allan C. Wechsler_, Dec 29 2014
</source_code></program><program><author>_Indranil Ghosh_</author><language_tag>(Python)</language_tag><file_ending>.py</file_ending><date>Mar 17 2017</date><source_code>
from sympy.ntheory import totient
print([totient(i) for i in range(1, 70)]) # _Indranil Ghosh_, Mar 17 2017
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Jun 03 2002</date><source_code> {a(n) = if( n&lt;1, n==0, 2^(n\2) / 2 + sumdiv(n, k, eulerphi(2*k) * 2^(n/k)) / (4*n))}; /* _Michael Somos_, Jun 03 2002 */
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [1 : n in [0..100]];
</source_code></program><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> {a(n) = 1};
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>May 07 2012</date><source_code>
a000012 = const 1
a000012_list = repeat 1 -- _Reinhard Zumkeller_, May 07 2012
</source_code></program><program><author>_Martin Ettl_</author><language_tag>(Maxima)</language_tag><file_ending>.lisp</file_ending><date>Nov 07 2012</date><source_code> makelist(1, n, 1, 30); /* _Martin Ettl_, Nov 07 2012 */
</source_code></program></computation>
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<?xml version='1.0' encoding='utf-8'?>
<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Oct 20 1999</date><source_code> {a(n) = if( n&lt;1, n==0, sumdiv(n, k, eulerphi(2*k) * 2^(n/k)) / (2*n))}; /* _Michael Somos_, Oct 20 1999 */
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Jul 08 2013</date><source_code>
a000013 0 = 1
a000013 n = sum (zipWith (*)
(map (a000010 . (* 2)) ds) (map (2 ^) $ reverse ds)) `div` (2 * n)
where ds = a027750_row n
-- _Reinhard Zumkeller_, Jul 08 2013
</source_code></program><program><author>_Indranil Ghosh_</author><language_tag>(Python)</language_tag><file_ending>.py</file_ending><date>Apr 28 2017</date><source_code>
from sympy import divisors, totient
def a(n): return 1 if n&lt;1 else sum([totient(2*d)*2**(n/d) for d in divisors(n)])/(2*n) # _Indranil Ghosh_, Apr 28 2017
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Dec 19 2014</date><source_code> {a(n) = my(A); if( n&lt;1, 0, A = x / (1 - x^2) + x * O(x^n); for(k=3, n-1, A /= (1 - x^k + x * O(x^n))^polcoeff(A, k)); polcoeff( (subst(A, x, x^2) * (1 - x) + A * (2 - A) * (1 + x)) / 2, n))}; /* _Michael Somos_, Dec 19 2014 */
</source_code></program></computation>
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<computation><program><author>_Michael Somos_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Jul 16 2002</date><source_code> {a(n) = if( n&lt;1, 0, while(matsize(factor(n))[1]&gt;1, n++); n)}; /* _Michael Somos_, Jul 16 2002 */
</source_code></program><program><author>_Charles R Greathouse IV_</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>Feb 01 2013</date><source_code> a(n)=if(n&gt;1,while(!isprimepower(n),n++));n \\ _Charles R Greathouse IV_, Feb 01 2013
</source_code></program><program><author>_Zerinvary Lajos_</author><language_tag>(Sage)</language_tag><file_ending>.sage</file_ending><date>Jun 13 2009</date><source_code> [next_prime_power(n) for n in range(72)] # _Zerinvary Lajos_, Jun 13 2009
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>Nov 17 2011</date><source_code>
a000015 n = a000015_list !! (n-1)
a000015_list = 1 : concat
(zipWith(\pp qq -&gt; replicate (fromInteger (pp - qq)) pp)
(tail a000961_list) a000961_list)
-- _Reinhard Zumkeller_, Nov 17 2011, Apr 25 2011
</source_code></program></computation>
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<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> a(n)=if(n&lt;1,n &gt;= 0,sumdiv(n,k,(k%2)*eulerphi(k)*2^(n/k))/(2*n));
</source_code></program><program><author>_Reinhard Zumkeller_</author><language_tag>(Haskell)</language_tag><file_ending>.hs</file_ending><date>May 01 2012</date><source_code>
a000016 0 = 1
a000016 n = (`div` (2 * n)) $ sum $
zipWith (*) (map a000010 oddDivs) (map ((2 ^) . (div n)) $ oddDivs)
where oddDivs = a182469_row n
-- _Reinhard Zumkeller_, May 01 2012
</source_code></program></computation>
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<computation />
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<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> a(n)=local(A);if(n&lt;0,0,A=qfrep([1,0;0,16],2^n);sum(k=1,2^n,A[k]!=0))
</source_code></program></computation>
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<?xml version='1.0' encoding='utf-8'?>
<computation><program><author>unknown</author><language_tag>(GAP)</language_tag><file_ending>.gap</file_ending><date>unknown</date><source_code> List([2..2499],NrPrimitiveGroups);
</source_code></program><program><author>unknown</author><language_tag>(MAGMA)</language_tag><file_ending>.m</file_ending><date>unknown</date><source_code> [NumberOfPrimitiveGroups(i) : i in [1..999]];
</source_code></program></computation>
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<?xml version='1.0' encoding='utf-8'?>
<computation><program><author>unknown</author><language_tag>(PARI)</language_tag><file_ending>.gp</file_ending><date>unknown</date><source_code> a(n)=if(n==1,2,eulerphi(2^n-1)/n) \\ Hauke Worpel (thebigh(AT)outgun.com), Jun 10 2008
</source_code></program></computation>
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