OFFSET
0,6
EXAMPLE
The strict partition (6,4,2,1) has 4 parts and 5 distinct divisors of parts {1,2,3,4,5}, so is counted under a(13).
The a(2) = 1 through a(11) = 10 partitions:
(2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
(3,2) (4,2) (4,3) (5,3) (5,4) (6,4) (6,5)
(4,1) (5,2) (6,2) (6,3) (7,3) (7,4)
(6,1) (4,3,1) (7,2) (8,2) (8,3)
(8,1) (9,1) (9,2)
(4,3,2) (5,3,2) (10,1)
(6,2,1) (5,4,1) (5,4,2)
(6,3,1) (6,3,2)
(6,4,1)
(8,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[Union[#]] < Length[Union@@Divisors/@#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2024
STATUS
approved