A358909 Number of integer partitions of n whose parts have weakly decreasing numbers of prime factors (A001222).

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 53, 73, 93, 124, 157, 206, 256, 329, 406, 514, 628, 784, 949, 1174, 1411, 1725, 2061, 2500, 2966, 3570, 4217, 5039, 5919, 7027, 8219, 9706, 11301, 13268, 15394, 17995, 20792, 24195, 27863, 32288, 37061, 42779, 48950, 56306

Offset

0,3

Comments

First differs from A000041 at a(9) = 29, A000041(9) = 30, the difference coming from the partition (5,4).

Links

Table of n, a(n) for n=0..48.

Mathematica

Table[Length[Select[IntegerPartitions[n], GreaterEqual@@PrimeOmega/@#&]], {n, 0, 30}]

Crossrefs

For sequences of partitions see A141199, compositions A218482.

The case of equality is A319169, for compositions A358911.

The case of compositions is A358335, strictly decreasing A358901.

The complement is counted by A358910.

A001222 counts prime factors, distinct A001221.

A011782 counts compositions.

A063834 counts twice-partitions.

Cf. A056239, A300335, A320324, A358831, A358903, A358908.

Sequence in context: A319475 A319454 A023029 * A035987 A035997 A036008

Adjacent sequences: A358906 A358907 A358908 * A358910 A358911 A358912

Keyword

nonn

Author

Gus Wiseman, Dec 09 2022

Status

approved