A324749 Number of strict integer partitions of n containing no part > 1 whose prime indices all belong to the partition.

1, 1, 1, 1, 2, 1, 3, 4, 3, 4, 6, 6, 8, 11, 10, 14, 14, 19, 21, 26, 28, 35, 38, 44, 50, 60, 65, 79, 88, 98, 113, 131, 144, 165, 185, 211, 234, 268, 297, 334, 374, 420, 470, 525, 584, 649, 727, 801, 902, 998, 1100, 1220, 1357, 1500, 1657, 1833, 2029, 2220, 2462

Offset

0,5

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..58.

Example

The a(0) = 1 through a(10) = 6 strict integer partitions:
  ()  (1)  (2)  (3)  (4)    (5)  (6)    (7)    (8)    (9)    (10)
                     (3,1)       (4,2)  (4,3)  (6,2)  (5,4)  (6,4)
                                 (5,1)  (5,2)  (7,1)  (6,3)  (7,3)
                                        (6,1)         (7,2)  (8,2)
                                                             (9,1)
                                                             (6,3,1)

Mathematica

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

Crossrefs

The subset version is A324738. The non-strict version is A324754. The Heinz number version is A324759. An infinite version is A324694.

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

Cf. A324744, A324750, A324755, A324760.

Sequence in context: A122530 A301453 A278340 * A022466 A144254 A378020

Adjacent sequences: A324746 A324747 A324748 * A324750 A324751 A324752

Keyword

nonn

Author

Gus Wiseman, Mar 15 2019

Status

approved