OFFSET
0,5
COMMENTS
These are partitions without ones such that it is possible to choose a different divisor of each part.
EXAMPLE
The a(0) = 1 through a(9) = 6 partitions:
() . (2) (3) (4) (5) (6) (7) (8) (9)
(2,2) (3,2) (3,3) (4,3) (4,4) (5,4)
(4,2) (5,2) (5,3) (6,3)
(3,2,2) (6,2) (7,2)
(3,3,2) (4,3,2)
(4,2,2) (5,2,2)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1] && Length[Select[Tuples[Divisors/@#], UnsameQ@@#&]]>0&]], {n, 0, 30}]
CROSSREFS
A000005 counts divisors.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 04 2024
STATUS
approved