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%I #5 Jul 17 2018 08:09:20
%S 2,195,3185,5467,6475,6815,8455,10527,15385,16401,17719,20445,20535,
%T 21045,25365,28897,40001,46155,49841,50431,54677,92449,101543,113849,
%U 123469,137731,156883,164255,171941,185803,218855,228085,230347,261457,267883,274261
%N Heinz numbers of integer partitions into relatively prime parts whose reciprocal sum is the reciprocal of 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).
%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e 5467 is the Heinz number of (20,5,4) and 1/20 + 1/5 + 1/4 = 1/2, so 5467 belongs to the sequence.
%e The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (6,3,2), (6,4,4,3), (20,5,4), (12,4,3,3), (15,10,3), (24,8,3), (10,5,5,2)
%t Select[Range[2,100000],And[GCD@@PrimePi/@FactorInteger[#][[All,1]]==1,IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]
%Y Cf. A000837, A002966, A051908, A058360, A100953, A289509, A296150, A316854, A316855, A316856, A316857, A316888-A316904.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 16 2018