A295576 a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^4.

0, 1, 1, 1, 17, 1, 98, 82, 273, 82, 979, 626, 2275, 707, 2674, 3108, 8772, 3027, 15333, 9044, 14994, 9669, 39974, 17668, 50085, 24310, 60597, 50470, 127687, 45604, 178312, 103496, 149908, 103496, 225302, 129750, 432345, 187017, 349830, 266088, 722666

Offset: 1

Author

N. J. A. Sloane, Dec 08 2017

Keywords

• nonn

Comments

If p is an odd prime, a(p) = p*(p^2-1)*(3*p^2-7)/480. - Robert Israel, Dec 10 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• John D. Baum, A Number-Theoretic Sum, Mathematics Magazine 55.2 (1982): 111-113.

Crossrefs

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.

Programs

Maple

f:= n -> add(t^4, t = select(t->igcd(t,n)=1, [$1..n/2])):
map(f, [$1..100]); # Robert Israel, Dec 10 2017

Mathematica

f[n_] := Plus @@ (Select[Range[n/2], GCD[#, n] == 1 &]^4); Array[f, 41] (* Robert G. Wilson v, Dec 10 2017 *)

PARI

a(n) = sum(j=1, n\2, (gcd(j, n)==1)*j^4); \\ Michel Marcus, Dec 10 2017