OFFSET
0,7
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.
EXAMPLE
The a(2) = 1 through a(17) = 12 strict integer partitions (A...H = 10...17):
2 3 4 5 6 7 8 9 A B C D E F G H
42 43 54 64 65 75 76 86 87 97 98
52 63 73 83 84 85 95 96 A6 A7
72 82 542 93 94 A4 A5 C4 B6
A2 B2 B3 B4 D3 C5
643 752 C3 E2 D4
842 D2 763 E3
654 943 854
843 A42 863
852 872
A52
B42
An example for n = 60 is (19,14,13,7,5,2), with prime indices:
19: {8}
14: {1,4}
13: {6}
7: {4}
5: {3}
2: {1}
None of these prime indices {1,3,4,6,8} belong to the partition, as required.
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MemberQ[#, 1]&&Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2019
STATUS
approved