OFFSET
0,4
COMMENTS
The Heinz numbers of these partitions are given by A371177.
Also partitions such that the number of distinct parts is equal to the number of distinct divisors of parts.
EXAMPLE
The partition (4,2,1,1) contains all distinct divisors {1,2,4}, so is counted under a(8).
The partition (4,4,3,2,2,2,1) contains all distinct divisors {1,2,3,4} so is counted under 4 + 4 + 3 + 2 + 2 + 2 + 1 = 18. - David A. Corneth, Mar 18 2024
The a(0) = 1 through a(8) = 12 partitions:
() (1) (11) (21) (31) (221) (51) (331) (71)
(111) (211) (311) (321) (421) (521)
(1111) (2111) (2211) (511) (3221)
(11111) (3111) (2221) (3311)
(21111) (3211) (4211)
(111111) (22111) (5111)
(31111) (22211)
(211111) (32111)
(1111111) (221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SubsetQ[#, Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2024
STATUS
approved