OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).
FORMULA
G.f.: Sum_{k>=1} (-1)^(k+1)*k^6*x^k/(1 + x^k). - Ilya Gutkovskiy, Nov 27 2018
Multiplicative with a(2^e) = -(31*2^(6*e+1) + 127)/63, and a(p^e) = (p^(6*e+6) - 1)/(p^6 - 1) for p > 2. - Amiram Eldar, Nov 22 2022
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^6 &]; Array[a, 50] (* Amiram Eldar, Nov 27 2018 *)
PROG
(PARI) apply( A321562(n)=sumdiv(n, d, (-1)^(n\d-d)*d^6), [1..30]) \\ M. F. Hasler, Nov 26 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&+[(-1)^(k+1)*k^6*x^k/(1 + x^k) : k in [1..2*m]]) )); // G. C. Greubel, Nov 28 2018
(Sage) s=(sum((-1)^(k+1)*k^6*x^k/(1 + x^k) for k in (1..50))).series(x, 50); a = s.coefficients(x, sparse=False); a[1:] # G. C. Greubel, Nov 28 2018
CROSSREFS
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved