A324756 Number of integer partitions of n containing no prime indices of the parts.

1, 1, 2, 2, 4, 3, 7, 7, 9, 11, 16, 16, 24, 25, 34, 39, 50, 54, 70, 79, 96, 111, 135, 152, 186, 208, 249, 285, 335, 377, 448, 506, 588, 664, 777, 873, 1010, 1139, 1309, 1471, 1697, 1890, 2175, 2435, 2772, 3106, 3532, 3941, 4478, 4995, 5643, 6297, 7107, 7897

Offset

0,3

Comments

These could be described as anti-transitive integer partitions.

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..53.

Example

The a(1) = 1 through a(8) = 9 integer partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (111)  (22)    (311)    (33)      (43)       (44)
                    (31)    (11111)  (42)      (52)       (71)
                    (1111)           (51)      (331)      (422)
                                     (222)     (511)      (2222)
                                     (3111)    (31111)    (3311)
                                     (111111)  (1111111)  (5111)
                                                          (311111)
                                                          (11111111)

Mathematica

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

Crossrefs

The subset version is A324741, with maximal case A324743. The strict case is A324751. The Heinz number version is A324758. An infinite version is A324695.

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

Sequence in context: A239832 A240010 A283502 * A324754 A174220 A334871

Adjacent sequences: A324753 A324754 A324755 * A324757 A324758 A324759

Keyword

nonn

Author

Gus Wiseman, Mar 17 2019

Status

approved