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A324750 Number of strict integer partitions of n not containing 1 or any part whose prime indices all belong to the partition. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A145394 A179806

Adjacent sequences:  A324747 A324748 A324749 * A324751 A324752 A324753

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 15 2019

STATUS

approved

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)