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%I #21 Dec 10 2017 19:11:34
%S 0,1,1,1,17,1,98,82,273,82,979,626,2275,707,2674,3108,8772,3027,15333,
%T 9044,14994,9669,39974,17668,50085,24310,60597,50470,127687,45604,
%U 178312,103496,149908,103496,225302,129750,432345,187017,349830,266088,722666
%N a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^4.
%C If p is an odd prime, a(p) = p*(p^2-1)*(3*p^2-7)/480. - _Robert Israel_, Dec 10 2017
%H Seiichi Manyama, <a href="/A295576/b295576.txt">Table of n, a(n) for n = 1..10000</a>
%H John D. Baum, <a href="http://www.jstor.org/stable/2690056">A Number-Theoretic Sum</a>, Mathematics Magazine 55.2 (1982): 111-113.
%p f:= n -> add(t^4, t = select(t->igcd(t,n)=1, [$1..n/2])):
%p map(f, [$1..100]); # _Robert Israel_, Dec 10 2017
%t f[n_] := Plus @@ (Select[Range[n/2], GCD[#, n] == 1 &]^4); Array[f, 41] (* _Robert G. Wilson v_, Dec 10 2017 *)
%o (PARI) a(n) = sum(j=1, n\2, (gcd(j, n)==1)*j^4); \\ _Michel Marcus_, Dec 10 2017
%Y 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 nonn
%O 1,5
%A _N. J. A. Sloane_, Dec 08 2017