%I #5 Mar 18 2019 08:13:23
%S 1,1,2,2,4,3,7,7,9,11,16,16,24,25,34,39,50,54,70,79,96,111,135,152,
%T 186,208,249,285,335,377,448,506,588,664,777,873,1010,1139,1309,1471,
%U 1697,1890,2175,2435,2772,3106,3532,3941,4478,4995,5643,6297,7107,7897
%N Number of integer partitions of n containing no prime indices of the parts.
%C These could be described as anti-transitive integer partitions.
%C 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.
%e The a(1) = 1 through a(8) = 9 integer partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (11) (111) (22) (311) (33) (43) (44)
%e (31) (11111) (42) (52) (71)
%e (1111) (51) (331) (422)
%e (222) (511) (2222)
%e (3111) (31111) (3311)
%e (111111) (1111111) (5111)
%e (311111)
%e (11111111)
%t Table[Length[Select[IntegerPartitions[n],Intersection[#,PrimePi/@First/@Join@@FactorInteger/@#]=={}&]],{n,0,30}]
%Y 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.
%Y Cf. A000720, A000837, A001462, A051424, A112798, A276625, A304360, A306844, A324764, A324742, A324753.
%K nonn
%O 0,3
%A _Gus Wiseman_, Mar 17 2019