A321563 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^7.

1, -129, 2188, -16257, 78126, -282252, 823544, -2080641, 4785157, -10078254, 19487172, -35570316, 62748518, -106237176, 170939688, -266321793, 410338674, -617285253, 893871740, -1270094382, 1801914272, -2513845188, 3404825448, -4552442508

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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).

Index entries for sequences mentioned by Glaisher.

Formula

G.f.: Sum_{k>=1} (-1)^(k+1)*k^7*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018

Multiplicative with a(2^e) = -3*(21*2^(7*e+1) + 85)/127, and a(p^e) = (p^(7*e+7) - 1)/(p^7 - 1) for p > 2. - Amiram Eldar, Nov 22 2022

Mathematica

a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^7 &]; Array[a, 25] (* Amiram Eldar, Nov 22 2022 *)

Prog

(PARI) apply( A321563(n)=sumdiv(n, d, (-1)^(n\d-d)*d^7), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

Column k=7 of A322083.

Cf. A321543 - A321565, A321807 - A321836 for similar sequences.

Sequence in context: A353940 A351270 A088719 * A034681 A351302 A017677

Adjacent sequences: A321560 A321561 A321562 * A321564 A321565 A321566

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved