A324753 - OEIS

A324753

Number of integer partitions of n containing all prime indices of their parts.

1, 1, 1, 2, 2, 4, 5, 7, 8, 14, 16, 23, 29, 40, 49, 66, 81, 109, 133, 172, 211, 274, 332, 419, 511, 640, 775, 965, 1165, 1434, 1730, 2109, 2530, 3083, 3683, 4447, 5308, 6375, 7573, 9062, 10730, 12786, 15104, 17909, 21095, 24937, 29284, 34488, 40421, 47450

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OFFSET

0,4

COMMENTS

These could be described as transitive integer partitions.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

The a(1) = 1 through a(8) = 8 integer partitions:

(1) (11) (21) (211) (41) (321) (421) (3221)

(111) (1111) (221) (411) (2221) (4211)