A321808 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^11.

1, -2049, 177148, -4192257, 48828126, -362976252, 1977326744, -8585738241, 31381236757, -100048830174, 285311670612, -742649943036, 1792160394038, -4051542498456, 8649804864648, -17583591913473, 34271896307634, -64300154115093

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^11*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018

Multiplicative with a(2^e) = -3*(341*2^(11*e+1) + 1365)/2047, and a(p^e) = (p^(11*e+11) - 1)/(p^11 - 1) for p > 2. - Amiram Eldar, Nov 22 2022

Mathematica

a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^11 &]; Array[a, 50] (* Amiram Eldar, Nov 22 2022 *)

Prog

(PARI) apply( A321808(n)=sumdiv(n, d, (-1)^(n\d-d)*d^11), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

Column k=11 of A322083.

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

Sequence in context: A071116 A060949 A230189 * A017685 A013959 A036089

Adjacent sequences: A321805 A321806 A321807 * A321809 A321810 A321811

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved