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%I #5 Jul 17 2018 08:09:26
%S 2,18,72,147,162,195,250,288,294,390,500,588,648,780,1125,1152,1176,
%T 1323,1458,1560,1755,2000,2250,2352,2592,2646,3120,3185,3510,4000,
%U 4500,4608,4704,4802,5292,6240,6370,6475,6591,7020,7581,8450,9000,9408,10101,10125
%N Heinz numbers of aperiodic integer partitions whose reciprocal sum is an integer.
%C The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A partition is aperiodic if its multiplicities are relatively prime.
%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (221), (22111), (442), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111).
%t Select[Range[2,20000],And[GCD@@FactorInteger[#][[All,2]]==1,IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]
%Y Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 16 2018
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