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%I #6 Mar 16 2019 10:12:41
%S 1,1,1,1,2,1,3,3,2,4,5,5,6,8,8,12,10,14,13,18,19,26,25,30,34,39,40,51,
%T 55,60,71,77,90,97,111,123,136,153,170,179,216,230,264,282,322,345,
%U 385,423,470,513,573,629,686,755,834,910,1005,1095,1194,1303,1433
%N Number of strict integer partitions of n containing no prime indices of the parts.
%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(13) = 8 strict integer partitions (A...D = 10...13):
%e 1 2 3 4 5 6 7 8 9 A B C D
%e 31 42 43 71 54 64 65 75 76
%e 51 52 63 73 83 84 85
%e 72 82 542 93 94
%e 91 731 A2 B2
%e B1 643
%e 751
%e 931
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Intersection[#,PrimePi/@First/@Join@@FactorInteger/@#]=={}&]],{n,0,30}]
%Y The subset version is A324741, with maximal case A324743. The non-strict version is A324756. The Heinz number version is A324758. An infinite version is A304360.
%Y Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A305713, A306844, A324764.
%Y Cf. A324695, A324742, A324748.
%K nonn
%O 0,5
%A _Gus Wiseman_, Mar 16 2019
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