OFFSET
0,3
COMMENTS
These could be described as anti-transitive integer partitions.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The a(1) = 1 through a(8) = 9 integer partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (311) (33) (43) (44)
(31) (11111) (42) (52) (71)
(1111) (51) (331) (422)
(222) (511) (2222)
(3111) (31111) (3311)
(111111) (1111111) (5111)
(311111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved