A321556 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^11.

1, 2047, 177148, 4192255, 48828126, 362621956, 1977326744, 8585738239, 31381236757, 99951173922, 285311670612, 742649588740, 1792160394038, 4047587844968, 8649804864648, 17583591913471, 34271896307634, 64237391641579

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} k^11*x^k/(1 + x^k). - Seiichi Manyama, Nov 25 2018

From Amiram Eldar, Nov 11 2022: (Start)

Multiplicative with a(2^e) = (1023*2^(11*e+1)+1)/2047, and a(p^e) = (p^(11*e+11) - 1)/(p^11 - 1) if p > 2.

Sum_{k=1..n} a(k) ~ c * n^12, where c = 2047*zeta(12)/24576 = 0.0833131... . (End)

Mathematica

f[p_, e_] := (p^(11*e + 11) - 1)/(p^11 - 1); f[2, e_] := (1023*2^(11*e + 1) + 1)/2047; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 11 2022 *)

Prog

(PARI) apply( A321556(n)=sumdiv(n, d, (-1)^(n\d-1)*d^11), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

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

Cf. A013670.

Sequence in context: A022527 A024009 A258812 * A321550 A014233 A160964

Adjacent sequences: A321553 A321554 A321555 * A321557 A321558 A321559

Keyword

nonn,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved