OFFSET
1,5
COMMENTS
The Heinz numbers of these partitions are given by A370348.
EXAMPLE
The partition (3,2,1,1) has 4 parts {1,2,3,4} and 3 distinct divisors of parts {1,2,3}, so is counted under a(7).
The a(0) = 0 through a(8) = 12 partitions:
. . (11) (111) (211) (221) (222) (331) (2222)
(1111) (311) (2211) (511) (3221)
(2111) (3111) (2221) (3311)
(11111) (21111) (3211) (4211)
(111111) (4111) (5111)
(22111) (22211)
(31111) (32111)
(211111) (41111)
(1111111) (221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#] > Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2024
STATUS
approved