%I #9 Sep 26 2019 09:05:05
%S 2,88,328,5128,9075,327688,1310728,2066056,2259976,188186624,
%T 560889856,847020032,1342177288
%N The sigma(EulerPhi)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.
%C These are all the terms less than 10^5. Problem: Find an expression generating all the terms.
%H J. Pe, <a href="http://jlpe.tripod.com/gpn/fperfect.htm">On a Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 168-172.
%e 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 f[x_] := DivisorSigma[1, EulerPhi[x]]; Select[ Range[ 1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]
%Y Cf. A000010, A000203, A066218.
%K nonn,more
%O 1,1
%A _Joseph L. Pe_, Dec 18 2001
%E a(6)-a(13) from _Amiram Eldar_, Sep 26 2019