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A324759 Heinz numbers of integer partitions containing no part > 1 whose prime indices all belong to the partition.

%I A324759 #4 Mar 18 2019 08:14:25
%S A324759 1,2,3,4,5,7,8,9,10,11,13,16,17,19,20,21,22,23,25,26,27,29,31,32,33,
%T A324759 34,35,37,39,40,41,43,44,46,47,49,50,51,52,53,57,58,59,61,62,63,64,65,
%U A324759 67,68,71,73,74,77,79,80,81,82,83,85,86,87,88,89,91,92,93
%N A324759 Heinz numbers of integer partitions containing no part > 1 whose prime indices all belong to the partition.
%C A324759 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. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e A324759 The sequence of terms together with their prime indices begins:
%e A324759    1: {}
%e A324759    2: {1}
%e A324759    3: {2}
%e A324759    4: {1,1}
%e A324759    5: {3}
%e A324759    7: {4}
%e A324759    8: {1,1,1}
%e A324759    9: {2,2}
%e A324759   10: {1,3}
%e A324759   11: {5}
%e A324759   13: {6}
%e A324759   16: {1,1,1,1}
%e A324759   17: {7}
%e A324759   19: {8}
%e A324759   20: {1,1,3}
%e A324759   21: {2,4}
%e A324759   22: {1,5}
%e A324759   23: {9}
%e A324759   25: {3,3}
%e A324759   26: {1,6}
%t A324759 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324759 Select[Range[100],!MemberQ[DeleteCases[primeMS[#],1],k_/;SubsetQ[primeMS[#],primeMS[k]]]&]
%Y A324759 The subset version is A324738, with maximal case A324744. The strict integer partition version is A324749. The integer partition version is A324754. An infinite version is A324694.
%Y A324759 Cf. A000720, A001221, A007097, A056239, A112798, A276625, A289509, A290822, A306844, A324695, A324750, A324755, A324760.
%K A324759 nonn
%O A324759 1,2
%A A324759 _Gus Wiseman_, Mar 17 2019