A321546 a(n) = Sum_{d|n} (-1)^(d-1)*d^7.

1, -127, 2188, -16511, 78126, -277876, 823544, -2113663, 4785157, -9922002, 19487172, -36126068, 62748518, -104590088, 170939688, -270549119, 410338674, -607714939, 893871740, -1289938386, 1801914272, -2474870844, 3404825448, -4624694644, 6103593751, -7969061786, 10465138360, -13597534984, 17249876310

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 23 2018

Multiplicative with a(2^e) = 2 - (2^(7*e + 7) - 1)/127, and a(p^e) = (p^(7*e + 7) - 1)/(p^7 - 1) for p > 2. - Amiram Eldar, Nov 04 2022

Mathematica

f[p_, e_] := (p^(7*e + 7) - 1)/(p^7 - 1); f[2, e_] := 2 - (2^(7*e + 7) - 1)/127; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 04 2022 *)

Prog

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

Crossrefs

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

Sequence in context: A024005 A258808 A321552 * A345458 A008398 A144969

Adjacent sequences: A321543 A321544 A321545 * A321547 A321548 A321549

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved