OFFSET
0,6
EXAMPLE
The partition (10,6,4) has unique choice (5,3,2) so is counted under a(20).
The a(0) = 1 through a(12) = 5 partitions:
() . (2) (3) (4) (5) . (7) (8) (9) (6,4) (11) (6,6)
(3,2) (4,3) (5,3) (5,4) (7,3) (7,4) (7,5)
(5,2) (6,2) (6,3) (5,3,2) (8,3) (10,2)
(7,2) (9,2) (5,4,3)
(7,3,2)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Union[Sort/@Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]]==1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 29 2024
STATUS
approved