A066226 The sigma(EulerPhi)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.

2, 88, 328, 5128, 9075, 327688, 1310728, 2066056, 2259976, 188186624, 560889856, 847020032, 1342177288

Offset

1,1

Comments

These are all the terms less than 10^5. Problem: Find an expression generating all the terms.

Links

Table of n, a(n) for n=1..13.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000010, A000203, A066218.

Sequence in context: A172736 A244386 A273520 * A058439 A058463 A364974

Adjacent sequences: A066223 A066224 A066225 * A066227 A066228 A066229

Keyword

nonn,more

Author

Joseph L. Pe, Dec 18 2001

Extensions

a(6)-a(13) from Amiram Eldar, Sep 26 2019

Status

approved