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A304713 Squarefree numbers whose prime indices are pairwise indivisible. Heinz numbers of strict integer partitions with pairwise indivisible parts.

%I A304713 #4 May 17 2018 21:37:05
%S A304713 1,2,3,5,7,11,13,15,17,19,23,29,31,33,35,37,41,43,47,51,53,55,59,61,
%T A304713 67,69,71,73,77,79,83,85,89,91,93,95,97,101,103,107,109,113,119,123,
%U A304713 127,131,137,139,141,143,145,149,151,155,157,161,163,165,167,173
%N A304713 Squarefree numbers whose prime indices are pairwise indivisible. Heinz numbers of strict integer partitions with pairwise indivisible parts.
%C A304713 A prime index of n is a number m such that prime(m) divides n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A304713 Sequence of entries together with their corresponding multiset multisystems (see A302242) begins:
%e A304713 1:  {}
%e A304713 2:  {{}}
%e A304713 3:  {{1}}
%e A304713 5:  {{2}}
%e A304713 7:  {{1,1}}
%e A304713 11: {{3}}
%e A304713 13: {{1,2}}
%e A304713 15: {{1},{2}}
%e A304713 17: {{4}}
%e A304713 19: {{1,1,1}}
%e A304713 23: {{2,2}}
%e A304713 29: {{1,3}}
%e A304713 31: {{5}}
%e A304713 33: {{1},{3}}
%e A304713 35: {{2},{1,1}}
%t A304713 Select[Range[300],SquareFreeQ[#]&&Select[Tuples[PrimePi/@First/@FactorInteger[#],2],UnsameQ@@#&&Divisible@@#&]==={}&]
%Y A304713 Cf. A000009, A005117, A006126, A056239, A073576, A285572, A285573, A293606, A293993, A302696, A302796, A303362, A303365, A304711.
%K A304713 nonn
%O A304713 1,2
%A A304713 _Gus Wiseman_, May 17 2018