OFFSET
0,5
COMMENTS
The Heinz numbers of these partitions are given by A371179.
EXAMPLE
The partition (4,3,1,1) has 3 distinct parts {1,3,4} and 4 distinct divisors of parts {1,2,3,4}, so is counted under a(9).
The a(0) = 0 through a(9) = 14 partitions:
. . (2) (3) (4) (5) (6) (7) (8) (9)
(22) (32) (33) (43) (44) (54)
(41) (42) (52) (53) (63)
(222) (61) (62) (72)
(411) (322) (332) (81)
(4111) (422) (333)
(431) (432)
(611) (441)
(2222) (522)
(41111) (621)
(3222)
(4311)
(6111)
(411111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Union[#]] < Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2024
STATUS
approved