A111865 Expansion of g.f. Product_{k>=1} 1/(1-x^sigma(k)).

1, 1, 1, 2, 3, 3, 5, 7, 9, 11, 14, 17, 24, 29, 36, 46, 57, 66, 85, 103, 125, 151, 182, 213, 264, 310, 368, 440, 524, 604, 724, 849, 998, 1164, 1363, 1573, 1854, 2136, 2481, 2879, 3336, 3807, 4427, 5079, 5844, 6698, 7695, 8754, 10072, 11451, 13075, 14898, 16988

Offset: 0

Author

Jon Perry, Nov 23 2005

Keywords

• nonn

Comments

Number of partitions of n into parts of size p = sigma(k) for some k, when there are A054973(p) kinds of part p.

Examples

			a(6) = 5 : We have sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(5)=6 so 111111, 1113, 114, 6 and 33.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Seiichi Manyama)

Crossrefs

Cf. A000203, A002191, A007609, A054973, A305320.

Programs

Maple

with(numtheory):
seq(coeff(series(mul(1/(1-x^sigma(k)),k=1..n), x,n+1),x,n),n=0..60); # Muniru A Asiru, May 31 2018

Mathematica

CoefficientList[ Series[Product[1/(1 - x^DivisorSigma[1, k]), {k, 47}], {x, 0, 52}], x] (* Robert G. Wilson v, Nov 25 2005 *)

PARI

lista(nn) = Vec(prod(k=1, nn, 1/(1-x^sigma(k))+ O(x^nn))) \\ Michel Marcus, May 30 2018

Formula

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

Extensions

More terms from Robert G. Wilson v, Nov 25 2005

a(0)=1 prepended by Seiichi Manyama, May 30 2018