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%I #5 Jul 16 2018 21:47:02
%S 2,147,195,3185,6475,6591,7581,10101,10527,16401,20445,20535,21045,
%T 25365,46155,107653,123823,142805,164255,164983,171941,218855,228085,
%U 267883,304175,312785,333925,333935,335405,343735,355355,390963,414295,442975,444925,455975
%N Heinz numbers of aperiodic integer partitions whose reciprocal sum is 1.
%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 Sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (4,4,2), (6,3,2), (6,4,4,3), (12,4,3,3), (6,6,6,2), (8,8,4,2), (12,6,4,2), (10,5,5,2), (20,5,4,2), (15,10,3,2), (12,12,3,2), (18,9,3,2), (24,8,3,2), (42,7,3,2).
%t Select[Range[2,100000],And[GCD@@FactorInteger[#][[All,2]]==1,Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]==1]&]
%Y Cf. A000837, A002966, A007916, A051908, A058360, A296150, A316854, A316855, A316856, A316857, A316888-A316904.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 16 2018