A321550 a(n) = Sum_{d|n} (-1)^(d-1)*d^11.

1, -2047, 177148, -4196351, 48828126, -362621956, 1977326744, -8594130943, 31381236757, -99951173922, 285311670612, -743375186948, 1792160394038, -4047587844968, 8649804864648, -17600780175359, 34271896307634, -64237391641579, 116490258898220, -204899955368226, 350279478046112

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 24 2018

Multiplicative with a(2^e) = 2 - (2^(11*e + 11) - 1)/2047, and a(p^e) = (p^(11*e + 11) - 1)/(p^11 - 1) for p > 2. - Amiram Eldar, Nov 04 2022

Mathematica

f[p_, e_] := (p^(11*e + 11) - 1)/(p^11 - 1); f[2, e_] := 2 - (2^(11*e + 11) - 1)/2047; 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^11), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

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

Sequence in context: A024009 A258812 A321556 * A014233 A160964 A022193

Adjacent sequences: A321547 A321548 A321549 * A321551 A321552 A321553

Keyword

sign,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved