A066228 The EulerPhi(sigma(EulerPhi))-perfect numbers, where the f-perfect numbers for an arithmetical function f are defined in A066218.

2, 4, 28, 40, 448, 500380

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) (2002-2003), 168-172.

Example

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.

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