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