OFFSET
0,4
EXAMPLE
The a(0) = 0 through a(7) = 12 partitions:
. (1) (11) (21) (22) (41) (33) (61)
(111) (31) (221) (42) (322)
(211) (311) (51) (331)
(1111) (2111) (222) (421)
(11111) (321) (511)
(411) (2221)
(2211) (3211)
(3111) (4111)
(21111) (22111)
(111111) (31111)
(211111)
(1111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 29 2024
STATUS
approved