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A318948 Number of ways to choose an integer partition of each factor in a factorization of n. 8
1, 2, 3, 9, 7, 17, 15, 40, 39, 56, 56, 126, 101, 165, 197, 336, 297, 496, 490, 774, 837, 1114, 1255, 1948, 2007, 2638, 3127, 4123, 4565, 6201, 6842, 9131, 10311, 12904, 14988, 19516, 21637, 26995, 31488, 39250, 44583, 55418, 63261, 77683, 89935, 108068, 124754 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..47.

FORMULA

Dirichlet g.f.: Product_{n > 1} 1 / (1 - P(n) / n^s) where P = A000041. [clarified by Ilya Gutkovskiy, Oct 26 2019]

EXAMPLE

The a(4) = 9 ways: (1+1)*(1+1), (1+1+1+1), (1+1)*(2), (2)*(1+1), (2+1+1), (2)*(2), (2+2), (3+1), (4).

MATHEMATICA

facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]];

Table[Sum[Times@@PartitionsP/@fac, {fac, facs[n]}], {n, 10}]

CROSSREFS

Cf. A000041, A001055, A001970, A063834, A065026, A066739, A066815, A121229, A281113, A284639, A318949.

Sequence in context: A244257 A171054 A205860 * A328424 A299773 A021421

Adjacent sequences:  A318945 A318946 A318947 * A318949 A318950 A318951

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 05 2018

STATUS

approved

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Last modified July 9 14:56 EDT 2020. Contains 335543 sequences. (Running on oeis4.)