%I
%S 2,3,5,7,9,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,79,
%T 81,83,89,97,101,103,107,109,113,125,127,131,137,139,149,151,157,163,
%U 167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251
%N Heinz numbers of integer partitions whose sum of reciprocals squared is the reciprocal of an integer.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%t Select[Range[2,1000],IntegerQ[1/Total[If[#==1,{},Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]^2]]]]&]
%Y Cf. A001222, A051908, A056239, A058360, A112798, A289506, A289507, A316854, A316855.
%Y Cf. A318584, A318585, A318586, A318587, A318588.
%K nonn
%O 1,1
%A _Gus Wiseman_, Aug 29 2018
