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%I #28 Nov 06 2023 02:16:04
%S 1,8,27,64,126,216,343,512,730,1008,1331,1728,2198,2744,3402,4096,
%T 4914,5840,6859,8064,9262,10648,12167,13824,15751,17584,19710,21952,
%U 24390,27216,29791,32768,35938,39312,43218,46720,50654,54872,59346
%N a(n) = Sum_{d|n, n/d=1 mod 4} d^3.
%H Amiram Eldar, <a href="/A050462/b050462.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert G. Wilson v)
%F From _Amiram Eldar_, Nov 05 2023: (Start)
%F a(n) = A007331(n) - A050466(n).
%F a(n) = A050471(n) + A050466(n).
%F a(n) = (A007331(n) + A050471(n))/2.
%F Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Pi^4/192 + A175572/2 = 1.00181129167264... . (End)
%t a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 1 &])^3]; Array[a, 39] (* _Robert G. Wilson v_, Mar 26 2015 *)
%t a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 1 &]; Array[a, 50] (* _Amiram Eldar_, Nov 05 2023 *)
%o (PARI) a(n) = sumdiv(n, d, ((n/d % 4)== 1)* d^3); \\ _Michel Marcus_, Mar 26 2015
%Y Cf. A007331, A050466, A050471, A175572.
%Y Cf. A050460, A050461, A050463.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Dec 23 1999
%E Offset changed from 0 to 1 by _Robert G. Wilson v_, Mar 27 2015
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