OFFSET
0,7
EXAMPLE
The a(0) = 0 through a(11) = 9 partitions:
. . . . (22) . (33) (322) (44) (333) (55) (443)
(42) (332) (432) (82) (533)
(222) (422) (522) (433) (542)
(2222) (3222) (442) (632)
(622) (722)
(3322) (3332)
(4222) (4322)
(22222) (5222)
(32222)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1] && Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 04 2024
STATUS
approved