This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066228 #15 Aug 18 2024 19:02:56
%S A066228 2,4,28,40,448,500380
%N A066228 The EulerPhi(sigma(EulerPhi))-perfect numbers, where the f-perfect numbers for an arithmetical function f are defined in A066218.
%C A066228 There are no terms between 449 and 10^5. Are there any more terms? Are there infinitely many?
%C A066228 No more terms below 10^9. - _Amiram Eldar_, Sep 26 2019
%H A066228 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 A066228 Let f(n) = EulerPhi(sigma(EulerPhi(n))). Proper divisors of 28 = {1, 2, 4, 7, 14}; the sum of their f-values = 1+1+2+4+4 = 12 = f(28); hence 28 belongs to the sequence.
%t A066228 f[x_] := EulerPhi[DivisorSigma[1, EulerPhi[x]]]; Select[ Range[ 1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]
%Y A066228 Cf. A000010, A000203, A066218.
%K A066228 nonn,more
%O A066228 1,1
%A A066228 _Joseph L. Pe_, Dec 18 2001
%E A066228 a(6) from _Amiram Eldar_, Sep 26 2019