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A316465 Heinz numbers of integer partitions such that every nonempty submultiset has an integer average.

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%I A316465 #16 Jul 06 2018 17:05:11
%S A316465 1,2,3,4,5,7,8,9,10,11,13,16,17,19,21,22,23,25,27,29,31,32,34,37,39,
%T A316465 41,43,46,47,49,53,55,57,59,61,62,64,67,68,71,73,79,81,82,83,85,87,89,
%U A316465 91,94,97,101,103,107,109,110,111,113,115,118,121,125,127,128
%N A316465 Heinz numbers of integer partitions such that every nonempty submultiset has an integer average.
%C A316465 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A316465 Supersequence of A000961. - _David A. Corneth_, Jul 06 2018
%e A316465 Sequence of partitions begins (), (1), (2), (1,1), (3), (4), (1,1,1), (2,2), (3,1), (5), (6), (1,1,1,1), (7), (8), (4,2), (5,1), (9), (3,3), (2,2,2).
%t A316465 Select[Range[100],And@@IntegerQ/@Mean/@Union[Rest[Subsets[If[#==1,{},Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]]]]&]
%Y A316465 Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316557.
%K A316465 nonn
%O A316465 1,2
%A A316465 _Gus Wiseman_, Jul 06 2018