A321809 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^12.

1, -4097, 531442, -16773121, 244140626, -2177317874, 13841287202, -68702695425, 282430067923, -1000244144722, 3138428376722, -8913940970482, 23298085122482, -56707753666594, 129746582562692, -281406240452609, 582622237229762

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^12*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018

Multiplicative with a(2^e) = -(2047*2^(12*e+1) + 8191)/4095, and a(p^e) = (p^(12*e+12) - 1)/(p^12 - 1) for p > 2. - Amiram Eldar, Nov 22 2022

Mathematica

a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^12 &]; Array[a, 50] (* Amiram Eldar, Nov 22 2022 *)

Prog

(PARI) apply( A321809(n)=sumdiv(n, d, (-1)^(n\d-d)*d^12), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

Column k=12 of A322083.

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

Sequence in context: A217196 A342685 A342686 * A017687 A013960 A036090

Adjacent sequences: A321806 A321807 A321808 * A321810 A321811 A321812

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved