cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A295575 a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^3.

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%I A295575 #21 Dec 10 2017 18:45:31
%S A295575 0,1,1,1,9,1,36,28,73,28,225,126,441,153,416,496,1296,469,2025,1100,
%T A295575 1710,1225,4356,1800,4959,2556,5581,4410,11025,3872,14400,8128,11090,
%U A295575 8128,15822,8910,29241,13041,21996,16400,44100,15426,53361,27830,33716,29161,76176,27936,77652,37828
%N A295575 a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^3.
%C A295575 If p is an odd prime, a(p) = (n^2-1)^2/64. - _Robert Israel_, Dec 10 2017
%H A295575 Seiichi Manyama, <a href="/A295575/b295575.txt">Table of n, a(n) for n = 1..10000</a>
%H A295575 John D. Baum, <a href="http://www.jstor.org/stable/2690056">A Number-Theoretic Sum</a>, Mathematics Magazine 55.2 (1982): 111-113.
%p A295575 f:= n -> add(t^3, t = select(t->igcd(t,n)=1, [$1..n/2])) :
%p A295575 map(f, [$1..100]); # _Robert Israel_, Dec 10 2017
%t A295575 f[n_] := Plus @@ (Select[Range[n/2], GCD[#, n] == 1 &]^3); Array[f, 50] (* _Robert G. Wilson v_, Dec 10 2017 *)
%o A295575 (PARI) a(n) = sum(j=1, n\2, (gcd(j, n)==1)*j^3); \\ _Michel Marcus_, Dec 10 2017
%Y A295575 In the Baum (1982) paper, S_1, S_2, S_3, S_4 are A023896, A053818, A053819, A053820, and S'_1, S'_2, S'_3, S'_4 are A066840, A295574, A295575, A295576.
%K A295575 nonn
%O A295575 1,5
%A A295575 _N. J. A. Sloane_, Dec 08 2017