A362627 Euler transform of sigma_n(n) (sum of n-th powers of divisors of n).

1, 1, 6, 34, 322, 3588, 52844, 900082, 18111465, 411941506, 10548286788, 298667744593, 9286665651198, 314077164671106, 11484692279345752, 451291302965764596, 18966834595501974235, 848853415894558707472, 40305029983754331855502, 2023571200162099967806430, 107109031661019664234558776

Offset

0,3

Links

Table of n, a(n) for n=0..20.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Euler Transform

Formula

G.f.: Product_{k>=1} 1/(1 - x^k)^sigma(k,k).

a(n) = (1/n)*Sum_{k=1..n} a(n-k)*b(k) for n>1, a(0)=1, where b(k) = Sum_{d|k} d*sigma(d,d).

Mathematica

a = Table[DivisorSigma[n, n], {n, 20}]; CoefficientList[Series[Product[1/(1 - x^m)^a[[m]], {m, 20}], {x, 0, 20}], x]

Crossrefs

Cf. A023887 (sigma_n(n)), A061256, A350503, A353233.

Sequence in context: A355887 A337350 A245466 * A284330 A125759 A062819

Adjacent sequences: A362624 A362625 A362626 * A362628 A362629 A362630

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 28 2023

Status

approved