OFFSET
0,10
COMMENTS
These are partitions without ones such that it is not possible to choose a different divisor of each part.
EXAMPLE
The a(6) = 1 through a(14) = 12 partitions:
(222) . (2222) (333) (3322) (3332) (3333) (4333) (4442)
(3222) (4222) (5222) (4422) (7222) (5333)
(22222) (32222) (6222) (33322) (5522)
(33222) (43222) (8222)
(42222) (52222) (33332)
(222222) (322222) (43322)
(44222)
(53222)
(62222)
(332222)
(422222)
(2222222)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1] && Length[Select[Tuples[Divisors/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 03 2024
STATUS
approved