A321547 a(n) = Sum_{d|n} (-1)^(d-1)*d^8.

1, -255, 6562, -65791, 390626, -1673310, 5764802, -16843007, 43053283, -99609630, 214358882, -431720542, 815730722, -1470024510, 2563287812, -4311810303, 6975757442, -10978587165, 16983563042, -25699675166, 37828630724, -54661514910, 78310985282, -110523811934, 152588281251, -208011334110

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 23 2018

Multiplicative with a(2^e) = 2 - (2^(8*e + 8) - 1)/255, and a(p^e) = (p^(8*e + 8) - 1)/(p^8 - 1) for p > 2. - Amiram Eldar, Nov 04 2022

Mathematica

f[p_, e_] := (p^(8*e + 8) - 1)/(p^8 - 1); f[2, e_] := 2 - (2^(8*e + 8) - 1)/255; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* Amiram Eldar, Nov 04 2022 *)

Prog

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

Crossrefs

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

Sequence in context: A024006 A258809 A321553 * A221970 A177897 A160913

Adjacent sequences: A321544 A321545 A321546 * A321548 A321549 A321550

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved