A324750 Number of strict integer partitions of n not containing 1 or any part whose prime indices all belong to the partition.

1, 0, 1, 1, 1, 1, 2, 3, 2, 4, 4, 4, 6, 8, 8, 11, 10, 15, 16, 19, 23, 27, 28, 35, 39, 47, 50, 63, 68, 77, 91, 102, 114, 130, 147, 169, 187, 213, 237, 268, 300, 336, 380, 422, 472, 525, 587, 647, 731, 810, 895, 996, 1102, 1227, 1355, 1498, 1661, 1818, 2020, 2221

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.

Links

Table of n, a(n) for n=0..59.

Example

The a(2) = 1 through a(17) = 15 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  62  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   A3   B3   B4   D3   C5
                                       642  B2   C2   C3   E2   D4
                                            643  752  D2   763  E3
                                            652  842  654  862  F2
                                                      762  943  854
                                                      843  A42  863
                                                      852       872
                                                                A43
                                                                A52
                                                                B42
                                                                6542

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MemberQ[#, 1]&&!MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 30}]

Crossrefs

The subset version is A324739. The non-strict version is A324755. The Heinz number version is A324760. An infinite version is A324694.

Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A304360, A305713, A306844.

Cf. A324696, A324737, A324742, A324744, A324764.

Sequence in context: A035662 A249870 A325404 * A320348 A336315 A145394

Adjacent sequences: A324747 A324748 A324749 * A324751 A324752 A324753

Keyword

nonn

Author

Gus Wiseman, Mar 15 2019

Status

approved