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

Author

Joseph L. Pe, Dec 18 2001

Keywords

• nonn
• more

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

Examples

			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.
		

Links

• J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

Crossrefs

Cf. A000010, A000203, A066218.

Programs

Mathematica

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

Extensions

a(6) from Amiram Eldar, Sep 26 2019