%I #8 Jul 15 2018 13:26:10
%S 2,9,125,147,195,2401,3185,4225,6475,6591,7581,10101,10527,16401,
%T 20445,20535,21045,25365,46155,107653,123823,142805,161051,164255,
%U 164983,171941,218855,228085,267883,304175,312785,333925,333935,335405,343735,355355,390963
%N Heinz numbers of 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).
%e Sequence of all integer partitions whose reciprocal sum is 1 begins: (1), (2,2), (3,3,3), (4,4,2), (6,3,2), (4,4,4,4), (6,4,4,3), (6,6,3,3), (12,4,3,3), (6,6,6,2), (8,8,4,2).
%t Select[Range[2,10000],Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]==1&]
%Y Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316856, A316857.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 14 2018
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