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%I #5 Jul 06 2018 17:05:18
%S 3,5,9,10,11,17,21,22,25,27,28,30,31,41,46,57,59,67,68,78,81,82,83,84,
%T 85,88,90,91,98,99,100,105,109,110,111,121,125,127,146,155,157,164,
%U 179,184,191,194,203,208,211,213,222,228,241,243,247,252,253,264,267
%N Heinz numbers of integer partitions whose average is a prime number.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e 60 = 2*2*3*5 has prime indices {1,1,2,3} with average 7/4, so 60 does not belong to the sequence.
%e 90 = 2*3*3*5 has prime indices {1,2,2,3} with average 8/2 = 4, so 90 belongs to the sequence.
%t Select[Range[100],PrimeQ[Mean[If[#==1,{},Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]]]&]
%Y Cf. A000040, A000041, A000607, A056239, A067538, A078175, A100118, A237984, A296150, A316313, A316413.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 05 2018
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