OFFSET
0,5
COMMENTS
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.
For example, (6,2) is such a partition because the prime indices of 6 are {1,2}, which do not all belong to the partition. On the other hand, (5,3) is not such a partition because the prime indices of 5 are {3}, and 3 belongs to the partition.
EXAMPLE
The a(2) = 1 through a(10) = 10 integer partitions (A = 10):
(2) (3) (4) (5) (6) (7) (8) (9) (A)
(22) (33) (43) (44) (54) (55)
(42) (52) (62) (63) (64)
(222) (422) (72) (73)
(2222) (333) (82)
(522) (433)
(442)
(622)
(4222)
(22222)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@If[k==1, {}, FactorInteger[k]]]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2019
STATUS
approved