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

Author

Gus Wiseman, Mar 15 2019

Keywords

• nonn

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.

Examples

			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)
		

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.

Programs

Mathematica

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