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%I #5 Mar 16 2019 10:12:26
%S 1,1,1,1,2,1,3,4,3,4,6,6,8,11,10,14,14,19,21,26,28,35,38,44,50,60,65,
%T 79,88,98,113,131,144,165,185,211,234,268,297,334,374,420,470,525,584,
%U 649,727,801,902,998,1100,1220,1357,1500,1657,1833,2029,2220,2462
%N Number of strict integer partitions of n containing no part > 1 whose prime indices all belong to the partition.
%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(0) = 1 through a(10) = 6 strict integer partitions:
%e () (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
%e (3,1) (4,2) (4,3) (6,2) (5,4) (6,4)
%e (5,1) (5,2) (7,1) (6,3) (7,3)
%e (6,1) (7,2) (8,2)
%e (9,1)
%e (6,3,1)
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,k_/;SubsetQ[#,PrimePi/@First/@FactorInteger[k]]]&]],{n,0,30}]
%Y The subset version is A324738. The non-strict version is A324754. The Heinz number version is A324759. An infinite version is A324694.
%Y Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A305713.
%Y Cf. A324744, A324750, A324755, A324760.
%K nonn
%O 0,5
%A _Gus Wiseman_, Mar 15 2019
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