A321565 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^9.

1, -513, 19684, -261633, 1953126, -10097892, 40353608, -133955073, 387440173, -1001953638, 2357947692, -5149983972, 10604499374, -20701400904, 38445332184, -68584996353, 118587876498, -198756808749, 322687697780, -511002214758

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^9*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018

Multiplicative with a(2^e) = -3*(85*2^(9*e+1) + 341)/511, and a(p^e) = (p^(9*e+9) - 1)/(p^9 - 1) for p > 2. - Amiram Eldar, Nov 22 2022

Mathematica

CoefficientList[Series[Sum[(-1)^(k+1) k^9 x^k/(1+x^k), {k, 20}], {x, 0, 20}], x] (* Harvey P. Dale, Apr 09 2019 *)
a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^9 &]; Array[a, 25] (* Amiram Eldar, Nov 22 2022 *)

Prog

(PARI) apply( A321565(n)=sumdiv(n, d, (-1)^(n\d-d)*d^9), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

Column k=9 of A322083.

Cf. A321543 - A321564, A321807 - A321836 for similar sequences.

Sequence in context: A223651 A353942 A351272 * A351304 A017681 A013957

Adjacent sequences: A321562 A321563 A321564 * A321566 A321567 A321568

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved