OFFSET
0,10
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 first 15 terms count the following integer partitions.
1: (1)
3: (2,1)
5: (4,1)
6: (3,2,1)
7: (4,2,1)
9: (8,1)
9: (6,2,1)
10: (4,3,2,1)
11: (8,2,1)
11: (5,3,2,1)
12: (9,2,1)
12: (7,4,1)
12: (6,3,2,1)
13: (8,4,1)
13: (6,4,2,1)
14: (8,3,2,1)
14: (7,4,2,1)
15: (12,2,1)
15: (9,3,2,1)
15: (8,4,2,1)
15: (5,4,3,2,1)
An example for n = 6 is (20,18,11,5,3,2,1), with prime indices:
20: {1,1,3}
18: {1,2,2}
11: {5}
5: {3}
3: {2}
2: {1}
1: {}
All of these prime indices {1,2,3,5} belong to the partition, as required.
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SubsetQ[#, PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#, 1]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2019
STATUS
approved