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%I #10 Aug 30 2018 08:36:26
%S 2,81,8775,64827,950625,1953125,7022925,9055935,21781575,36020025,
%T 50124555,51883209,57909033,102984375,118978125,760816875,816747435,
%U 981059625,1206902781,1265058675,1387132263,2359670625,3902169375,4868424351,5222768733,5430160125
%N Heinz numbers of integer partitions whose sum of reciprocals squared is 1.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e The sequence of integer partitions with Heinz numbers in this sequence begins: (1), (2222), (633222), (4444222), (66333322).
%t Select[Range[100000],Total[If[#==1,{},Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]^2]]]==1&]
%Y Cf. A001222, A051908, A056239, A112798, A289506, A289507, A316855, A316856, A316857.
%Y Cf. A318584, A318585, A318586, A318588, A318589.
%K nonn
%O 1,1
%A _Gus Wiseman_, Aug 29 2018
%E a(6)-a(26) from _Alois P. Heinz_, Aug 30 2018
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