login
A324748
Number of strict integer partitions of n containing all prime indices of the parts.
10
1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 3, 2, 2, 4, 3, 4, 3, 5, 6, 9, 8, 7, 8, 11, 12, 13, 15, 17, 22, 22, 20, 28, 31, 32, 36, 41, 43, 53, 53, 59, 70, 76, 77, 89, 99, 108, 124, 135, 139, 160, 172, 188, 209, 229, 243, 274, 298, 315, 353, 391, 417, 457, 496, 538, 588
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
The subset version is A324736. The non-strict version is A324753. The Heinz number version is A290822. An infinite version is A324698.
Sequence in context: A029267 A111725 A302257 * A320387 A304707 A112218
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2019
STATUS
approved