Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jul 06 2018 17:05:11
%S 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 41,43,46,47,49,53,55,57,59,61,62,64,67,68,71,73,79,81,82,83,85,87,89,
%U 91,94,97,101,103,107,109,110,111,113,115,118,121,125,127,128
%N Heinz numbers of integer partitions such that every nonempty submultiset has an integer average.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C Supersequence of A000961. - _David A. Corneth_, Jul 06 2018
%e 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 Select[Range[100],And@@IntegerQ/@Mean/@Union[Rest[Subsets[If[#==1,{},Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]]]]&]
%Y Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316557.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 06 2018