%I
%S 1,15,82,239,626,1230,2402,3823,6643,9390,14642,19598,28562,36030,
%T 51332,61167,83522,99645,130322,149614,196964,219630,279842,313486,
%U 391251,428430,538084,574078,707282,769980,923522,978671,1200644,1252830,1503652,1587677
%N a(n) = Sum_{dn} (1)^(n/d+1)*d^4.
%C Multiplicative because this sequence is the Dirichlet convolution of A000583 and A062157 which are both multiplicative.  _Andrew Howroyd_, Jul 20 2018
%H Seiichi Manyama, <a href="/A284900/b284900.txt">Table of n, a(n) for n = 1..10000</a>
%H J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&pg=RA1PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 162 (see p. 4 and p. 8).
%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>
%F G.f.: Sum_{k>=1} k^4*x^k/(1 + x^k).  _Ilya Gutkovskiy_, Apr 07 2017
%t Table[Sum[(1)^(n/d + 1)*d^4, {d, Divisors[n]}], {n, 50}] (* _Indranil Ghosh_, Apr 05 2017 *)
%o (PARI) a(n) = sumdiv(n, d, (1)^(n/d + 1)*d^4); \\ _Indranil Ghosh_, Apr 05 2017
%o (Python)
%o from sympy import divisors
%o print [sum([(1)**(n/d + 1)*d**4 for d in divisors(n)]) for n in range(1, 51)] # _Indranil Ghosh_, Apr 05 2017
%Y Sum_{dn} (1)^(n/d+1)*d^k: A000593 (k=1), A078306 (k=2), A078307 (k=3), this sequence (k=4), A284926 (k=5), A284927 (k=6).
%Y Cf. A000583, A062157.
%K nonn,mult
%O 1,2
%A _Seiichi Manyama_, Apr 05 2017
