A324757 Number of integer partitions of n not containing 1 or any prime indices of the parts.

1, 0, 1, 1, 2, 1, 4, 3, 4, 6, 9, 7, 14, 12, 19, 21, 28, 29, 41, 45, 56, 64, 81, 89, 114, 125, 154, 176, 211, 236, 288, 324, 383, 432, 514, 578, 678, 766, 891, 1006, 1176, 1306, 1525, 1711, 1966, 2212, 2538, 2839, 3258, 3646, 4150, 4647, 5288, 5891, 6698, 7472

Offset: 0

Author

Gus Wiseman, Mar 17 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(2) = 1 through a(10) = 9 integer partitions:
  (2)  (3)  (4)   (5)  (6)    (7)   (8)     (9)    (A)
            (22)       (33)   (43)  (44)    (54)   (55)
                       (42)   (52)  (422)   (63)   (64)
                       (222)        (2222)  (72)   (73)
                                            (333)  (82)
                                            (522)  (433)
                                                   (442)
                                                   (4222)
                                                   (22222)
		

Crossrefs

The subset version is A324742, with maximal case A324763. The strict case is A324752. The Heinz number version is A324761. An infinite version is A324695.

Cf. A000720, A000837, A001462, A051424, A112798, A276625, A290822, A304360, A306844, A324764, A324742, A324753, A324756.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],!MemberQ[#,1]&&Intersection[#,PrimePi/@First/@Join@@FactorInteger/@#]=={}&]],{n,0,30}]