A321564 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^8.

1, -257, 6562, -65281, 390626, -1686434, 5764802, -16711425, 43053283, -100390882, 214358882, -428373922, 815730722, -1481554114, 2563287812, -4278124289, 6975757442, -11064693731, 16983563042, -25500455906, 37828630724, -55090232674

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^8*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018

Multiplicative with a(2^e) = -(127*2^(8*e+1) + 511)/255, and a(p^e) = (p^(8*e+8) - 1)/(p^8 - 1) for p > 2. - Amiram Eldar, Nov 22 2022

Mathematica

a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^8 &]; Array[a, 25] (* Amiram Eldar, Nov 22 2022 *)

Prog

(PARI) apply( A321564(n)=sumdiv(n, d, (-1)^(n\d-d)*d^8), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

Column k=8 of A322083.

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

Sequence in context: A353941 A351271 A155468 * A034682 A351303 A017679

Adjacent sequences: A321561 A321562 A321563 * A321565 A321566 A321567

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved