OFFSET
0,8
COMMENTS
The Heinz numbers of these partitions are given by A371165.
EXAMPLE
The partition (8,6,6) has 6 submultisets {(8,6,6),(8,6),(6,6),(8),(6),()} and 6 distinct divisors of parts {1,2,3,4,6,8}, so is counted under a(20).
The a(17) = 2 through a(24) = 9 partitions:
(17) (9,9) (19) (11,9) (14,7) (13,9) (23) (21,3)
(13,4) (15,3) (15,5) (17,4) (21,1) (19,4) (22,2)
(6,6,6) (8,6,6) (8,8,6) (22,1) (8,8,8)
(12,3,3) (12,4,4) (10,6,6) (15,4,4) (10,8,6)
(18,1,1) (16,3,3) (12,10,1) (12,6,6)
(18,2,2) (12,7,5)
(20,1,1) (18,3,3)
(20,2,2)
(12,10,2)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Divisors[Times@@Prime/@#]] == Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2024
STATUS
approved