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

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.

Sequence in context: A288248 A159804 A363671 * A104567 A347711 A087824

Adjacent sequences: A330992 A330993 A330994 * A330996 A330997 A330998

Keyword

nonn,frac

Author

Gus Wiseman, Jan 08 2020

Status

approved