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A324756
Number of integer partitions of n containing no prime indices of the parts.
31
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.
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.
Sequence in context: A239832 A240010 A283502 * A373516 A324754 A174220
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved