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.

A050463 a(n) = Sum_{d|n, n/d=1 mod 4} d^4.

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%I A050463 #20 Nov 06 2023 02:16:34
%S A050463 1,16,81,256,626,1296,2401,4096,6562,10016,14641,20736,28562,38416,
%T A050463 50706,65536,83522,104992,130321,160256,194482,234256,279841,331776,
%U A050463 391251,456992,531522,614656,707282,811296,923521,1048576,1185922
%N A050463 a(n) = Sum_{d|n, n/d=1 mod 4} d^4.
%H A050463 Seiichi Manyama, <a href="/A050463/b050463.txt">Table of n, a(n) for n = 1..10000</a>
%F A050463 From _Amiram Eldar_, Nov 05 2023: (Start)
%F A050463 a(n) = A285989(n) - A050467(n).
%F A050463 a(n) = A050468(n) + A050467(n).
%F A050463 a(n) = (A050468(n) + A285989(n))/2.
%F A050463 Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = 5*Pi^5/3072 + 31*zeta(5)/64 = 1.000340795436113... . (End)
%t A050463 a[n_] := DivisorSum[n, #^4 &, Mod[n/#, 4] == 1 &]; Array[a, 50] (* _Amiram Eldar_, Jul 08 2023 *)
%o A050463 (PARI) a(n) = sumdiv(n, d, (n/d % 4 == 1) * d^4); \\ _Amiram Eldar_, Nov 05 2023
%Y A050463 Cf. A050448, A050467, A050468, A013663, A285989.
%Y A050463 Cf. A050460, A050461, A050462.
%K A050463 nonn,easy
%O A050463 1,2
%A A050463 _N. J. A. Sloane_, Dec 23 1999
%E A050463 Offset changed from 0 to 1 by _Seiichi Manyama_, Jul 08 2023