A330996 Nearest integer to P(n)/Q(n) = A000041(n)/A000009(n).

1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 30, 32, 34, 35, 37, 39, 41, 44, 46, 48, 51, 53, 56, 59, 61, 64, 68, 71, 74, 78, 81, 85, 89, 93, 97, 101, 106, 111, 115, 120, 126

Offset: 0

Author

Gus Wiseman, Jan 08 2020

Keywords

• nonn

Comments

Conjecture: This sequence is nondecreasing. More generally, the rational sequence A000041(n)/A000009(n) is nondecreasing for n > 5.

Crossrefs

The numerators are A330994.

The denominators are A330995.

The same for factorizations is A331048.

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

Programs

Mathematica

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