

A066228


The EulerPhi(sigma(EulerPhi))perfect numbers, where the fperfect numbers for an arithmetical function f are defined in A066218.


0




OFFSET

1,1


COMMENTS

There are no terms between 449 and 10^5. Are there any more terms? Are there infinitely many?
No more terms below 10^9.  Amiram Eldar, Sep 26 2019


LINKS

Table of n, a(n) for n=1..6.
J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (20022003), 168172.


EXAMPLE

Let f(n) = EulerPhi(sigma(EulerPhi(n)). Proper divisors of 28 = {1, 2, 4, 7, 14}; the sum of their fvalues = 1+1+2+4+4 = 12 = f(28); hence 28 belongs to the sequence.


MATHEMATICA

f[x_] := EulerPhi[DivisorSigma[1, EulerPhi[x]]]; Select[ Range[ 1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]


CROSSREFS

Cf. A000010, A000203, A066218.
Sequence in context: A305738 A323447 A227303 * A110881 A156449 A259375
Adjacent sequences: A066225 A066226 A066227 * A066229 A066230 A066231


KEYWORD

nonn,more


AUTHOR

Joseph L. Pe, Dec 18 2001


EXTENSIONS

a(6) from Amiram Eldar, Sep 26 2019


STATUS

approved



