OFFSET
0,5
COMMENTS
The Heinz numbers of these partitions are given by A370802.
EXAMPLE
The partition (6,2,2,1) has 4 parts and 4 distinct divisors of parts {1,2,3,6} so is counted under a(11).
The a(1) = 1 through a(11) = 11 partitions:
(1) . (21) (22) . (33) (322) (71) (441) (55) (533)
(31) (51) (421) (332) (522) (442) (722)
(321) (422) (531) (721) (731)
(411) (521) (4311) (4321) (911)
(6111) (6211) (4322)
(4331)
(5321)
(5411)
(6221)
(6311)
(8111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]==Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2024
STATUS
approved