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

Author

Gus Wiseman, Jan 08 2020

Keywords

• nonn
• frac

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.

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.

Programs

Mathematica

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

Formula

A330994/A330995 = A000041/A000009.