A330995 - OEIS

A330995

Denominator P(n)/Q(n) = A000041(n)/A000009(n).

1, 1, 1, 2, 2, 3, 4, 1, 3, 4, 5, 3, 15, 18, 22, 27, 32, 38, 46, 27, 64, 19, 89, 104, 122, 71, 55, 96, 111, 256, 74, 170, 130, 64, 256, 195, 668, 760, 864, 982, 53, 60, 713, 1610, 1816, 1024, 384, 185, 970, 3264, 1829, 4097, 4582, 5120, 5718, 3189, 7108, 2639

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OFFSET

0,4

COMMENTS

An integer partition of n is a finite, nonincreasing sequence of positive integers (parts) summing to n. It is strict if the parts are all different. Integer partitions and strict integer partitions are counted by A000041 and A000009 respectively.

Conjecture: The only 1's occur at n = 0, 1, 2, 7.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

A330994/A330995 = A000041/A000009.

MATHEMATICA

Table[PartitionsP[n]/PartitionsQ[n], {n, 0, 100}]//Denominator

CROSSREFS

The numerators are A330994.

The rounded quotients are A330996.

The same for factorizations is A331024.

Cf. A000009, A000041, A001055, A003238, A005117, A035359, A045778, A046063, A331022.