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A318719 Heinz numbers of strict integer partitions in which no two parts are relatively prime.

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%I A318719 #6 Sep 02 2018 17:08:13
%S A318719 1,2,3,5,7,11,13,17,19,21,23,29,31,37,39,41,43,47,53,57,59,61,65,67,
%T A318719 71,73,79,83,87,89,91,97,101,103,107,109,111,113,115,127,129,131,133,
%U A318719 137,139,149,151,157,159,163,167,173,179,181,183,185,191,193,197
%N A318719 Heinz numbers of strict integer partitions in which no two parts are relatively prime.
%C A318719 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%t A318719 Select[Range[200],And[SquareFreeQ[#],And@@(GCD[##]>1&)@@@Select[Tuples[PrimePi/@FactorInteger[#][[All,1]],2],Less@@#&]]&]
%Y A318719 Cf. A302797, A303140, A303282, A303283, A305713, A305843, A318717, A318715, A318716, A318717.
%K A318719 nonn
%O A318719 1,2
%A A318719 _Gus Wiseman_, Sep 02 2018