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

0,5

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..55.

Example

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)

Mathematica

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

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.

Sequence in context: A116449 A316433 A071046 * A144334 A141210 A244373

Adjacent sequences: A324754 A324755 A324756 * A324758 A324759 A324760

Keyword

nonn

Author

Gus Wiseman, Mar 17 2019

Status

approved