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%I #6 Aug 30 2018 08:36:19
%S 1,2,4,8,16,32,64,81,128,162,256,324,512,648,1024,1296,2048,2592,4096,
%T 5184,6561,8192,8775,10368,13122,16384,17550,20736,26244,32768,35100,
%U 41472,52488,64827,65536,70200,82944,104976,129654,131072,140400,165888,209952
%N Heinz numbers of integer partitions whose sum of reciprocals squared is an integer.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e Sequence of integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (11), (111), (1111), (11111), (111111), (2222), (1111111), (22221), (11111111), (222211), (111111111), (2222111).
%t Select[Range[10000],IntegerQ[Total[If[#==1,{},Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]^2]]]]&]
%Y Cf. A001222, A056239, A058360, A112798, A289506, A289507, A316855, A316857.
%Y Cf. A318584, A318585, A318586, A318587, A318589.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 29 2018
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