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A324925
Number of integer partitions y of n such that Product_{i in y} prime(i)/i is an integer.
14
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
OFFSET
0,4
COMMENTS
The Heinz numbers of these integer partitions are given by A324850.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 20 2019
STATUS
approved