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A111865
Expansion of g.f. Product_{k>=1} 1/(1-x^sigma(k)).
4
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
0,4
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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Seiichi Manyama)
FORMULA
G.f.: Product_{k>=1} 1/(1-x^sigma(k)).
EXAMPLE
a(6) = 5 : We have sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(5)=6 so 111111, 1113, 114, 6 and 33.
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 *).
PROG
(PARI) lista(nn) = Vec(prod(k=1, nn, 1/(1-x^sigma(k))+ O(x^nn))) \\ Michel Marcus, May 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 23 2005
EXTENSIONS
More terms from Robert G. Wilson v, Nov 25 2005
a(0)=1 prepended by Seiichi Manyama, May 30 2018
STATUS
approved