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The sigma(EulerPhi)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.
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%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