A324925 - OEIS

A324925

Number of integer partitions y of n such that Product_{i in y} prime(i)/i is an integer.

1, 1, 1, 2, 2, 2, 5, 5, 5, 8, 9, 11, 17, 19, 21, 28, 32, 40, 51, 57, 67, 83, 96, 118, 142, 160, 189, 224, 260, 307, 363, 412, 479, 561, 649, 749, 874, 997, 1141, 1321, 1518, 1734, 1994, 2274, 2582, 2960, 3374, 3837, 4370, 4950, 5604, 6371, 7208, 8157, 9231, 10392

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OFFSET

0,4

COMMENTS

The Heinz numbers of these integer partitions are given by A324850.

LINKS

Table of n, a(n) for n=0..55.

EXAMPLE

The a(1) = 1 through a(8) = 5 integer partitions:

(1) (11) (21) (211) (2111) (321) (3211) (32111)

(111) (1111) (11111) (411) (4111) (41111)

(2211) (22111) (221111)

(21111) (211111) (2111111)

(111111) (1111111) (11111111)

For example, (3,2,1,1) is such a partition because (2/1) * (2/1) * (3/2) * (5/3) = 10 is an integer.

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], IntegerQ[Product[Prime[i]/i, {i, #}]]&]], {n, 0, 30}]

CROSSREFS

Cf. A003963, A109129, A324850, A324922, A324923, A324924, A324931, A324934.

Sequence in context: A308772 A332966 A035643 * A163946 A240500 A344264

Adjacent sequences: A324922 A324923 A324924 * A324926 A324927 A324928

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 20 2019

STATUS

approved