A324748 Number of strict integer partitions of n containing all prime indices of the parts.

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.

Links

Table of n, a(n) for n=0..66.

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.

Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A279861, A290689, A290760, A305713.

Cf. A324697, A324737, A324751.

Sequence in context: A029267 A111725 A302257 * A320387 A304707 A112218

Adjacent sequences: A324745 A324746 A324747 * A324749 A324750 A324751

Keyword

nonn

Author

Gus Wiseman, Mar 15 2019

Status

approved