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A324761 Heinz numbers of integer partitions not containing 1 or any prime indices of the parts.

%I A324761 #6 Mar 18 2019 08:14:40
%S A324761 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,33,35,37,41,43,47,49,51,53,
%T A324761 57,59,61,63,65,67,71,73,77,79,81,83,85,87,89,91,93,95,97,99,101,103,
%U A324761 107,109,113,115,121,123,125,127,129,131,133,137,139,143,147,149
%N A324761 Heinz numbers of integer partitions not containing 1 or any prime indices of the parts.
%C A324761 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 A324761 The sequence of terms together with their prime indices begins:
%e A324761    1: {}
%e A324761    3: {2}
%e A324761    5: {3}
%e A324761    7: {4}
%e A324761    9: {2,2}
%e A324761   11: {5}
%e A324761   13: {6}
%e A324761   17: {7}
%e A324761   19: {8}
%e A324761   21: {2,4}
%e A324761   23: {9}
%e A324761   25: {3,3}
%e A324761   27: {2,2,2}
%e A324761   29: {10}
%e A324761   31: {11}
%e A324761   33: {2,5}
%e A324761   35: {3,4}
%e A324761   37: {12}
%e A324761   41: {13}
%e A324761   43: {14}
%t A324761 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324761 Select[Range[1,100,2],Intersection[primeMS[#],Union@@primeMS/@primeMS[#]]=={}&]
%Y A324761 The subset version is A324742, with maximal case A324763. The strict integer partition version is A324752. The integer partition version is A324757. An infinite version is A324695.
%Y A324761 Cf. A000720, A001221, A007097, A056239, A112798, A276625, A289509, A290822, A304360, A306844, A324743, A324751, A324756, A324758, A324764.
%K A324761 nonn
%O A324761 1,2
%A A324761 _Gus Wiseman_, Mar 17 2019