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A316903 Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.

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%I A316903 #5 Jul 17 2018 08:09:36
%S A316903 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,65,67,71,73,79,83,
%T A316903 89,97,101,103,107,109,113,127,131,137,139,147,149,151,157,163,167,
%U A316903 173,179,181,191,193,195,197,199,211,223,227,229,233,239,241,251,257
%N A316903 Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.
%C A316903 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%C A316903 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A316903 A partition is aperiodic if its multiplicities are relatively prime.
%H A316903 Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%t A316903 Select[Range[2,1000],And[GCD@@FactorInteger[#][[All,2]]==1,IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]
%Y A316903 Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.
%K A316903 nonn
%O A316903 1,1
%A A316903 _Gus Wiseman_, Jul 16 2018