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%I #6 Jul 17 2018 08:09:12
%S 2,4,8,16,18,32,36,64,72,128,144,162,195,250,256,288,294,324,390,500,
%T 512,576,588,648,780,1000,1024,1125,1152,1176,1296,1458,1560,1755,
%U 2000,2048,2250,2304,2352,2592,2646,2916,3120,3185,3510,4000,4096,4500,4608
%N Heinz numbers of integer partitions into relatively prime parts 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).
%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), (11), (111), (1111), (221), (11111), (2211), (111111), (22111), (1111111), (221111), (22221), (632), (3331), (11111111).
%t Select[Range[2,1000],And[GCD@@PrimePi/@FactorInteger[#][[All,1]]==1,IntegerQ[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
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