cp's OEIS Frontend

A050466 a(n) = Sum_{d|n, n/d=3 mod 4} d^3.

%I A050466 #27 Nov 06 2023 02:18:12
%S A050466 0,0,1,0,0,8,1,0,27,0,1,64,0,8,126,0,0,216,1,0,370,8,1,512,0,0,730,64,
%T A050466 0,1008,1,0,1358,0,126,1728,0,8,2198,0,0,2960,1,64,3402,8,1,4096,343,
%U A050466 0,4914,0,0,5840,126,512,6886,0,1,8064,0,8,9991,0
%N A050466 a(n) = Sum_{d|n, n/d=3 mod 4} d^3.
%C A050466 From _Robert G. Wilson v_, Mar 26 2015: (Start)
%C A050466 a(n) = 0 for n = 1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 25, ... (A072437).
%C A050466 a(n) = 1 for n = 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, ... (A002145). (End)
%H A050466 Amiram Eldar, <a href="/A050466/b050466.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert G. Wilson v)
%F A050466 From _Amiram Eldar_, Nov 05 2023: (Start)
%F A050466 a(n) = A007331(n) - A050462(n).
%F A050466 a(n) = A050462(n) - A050471(n).
%F A050466 a(n) = (A007331(n) - A050471(n))/2.
%F A050466 Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Pi^4/192 - A175572/2 = 0.0128667399315... . (End)
%t A050466 a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 3 &])^3]; Array[a, 64] (* _Robert G. Wilson v_, Mar 26 2015 *)
%t A050466 a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 3 &]; Array[a, 50] (* _Amiram Eldar_, Nov 05 2023 *)
%o A050466 (PARI) a(n) = sumdiv(n, d, ((n/d % 4)== 3)* d^3); \\ _Michel Marcus_, Mar 26 2015
%Y A050466 Cf. A007331, A050462, A050471, A175572.
%Y A050466 Cf. A050464, A050465, A050467.
%Y A050466 Cf. A002145, A072437.
%K A050466 nonn,easy
%O A050466 1,6
%A A050466 _N. J. A. Sloane_, Dec 23 1999
%E A050466 Offset changed from 0 to 1 by _Robert G. Wilson v_, Mar 27 2015