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%I A066226
%S A066226 2,88,328,5128,9075
%N A066226 The sigma(EulerPhi)-perfect numbers, where the set of f-perfect numbers 
               for an arithmetical function f is defined in A066218.
%C A066226 These are all the terms less than 10^5. Problem: Find an expression generating 
               all the terms.
%H A066226 J. Pe, <a href="http://www.numeratus.netfperfect/fperfect.html">On a 
               Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 
               168-172.
%e A066226 Let f(n) = sigma(EulerPhi(n)). The proper divisors of 88 are {1, 2, 4, 
               8, 11, 22, 44}; adding their f-values: 1 + 1 + 3 + 7 + 18 + 18 + 
               42 = 90 = f(88). Hence 88 is a term of the sequence.
%t A066226 f[x_] := DivisorSigma[1, EulerPhi[x]]; Select[ Range[ 1, 10^5], 2 * f[ 
               # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]
%Y A066226 Sequence in context: A101578 A041881 A076542 this_sequence A058439 A058463 
               A166848
%Y A066226 Adjacent sequences: A066223 A066224 A066225 this_sequence A066227 A066228 
               A066229
%K A066226 nonn
%O A066226 1,1
%A A066226 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 18 2001

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