A316465 - 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