A091847 Perfect totient numbers, omitting powers of 3.

15, 39, 111, 183, 255, 327, 363, 471, 2199, 3063, 4359, 4375, 5571, 8751, 15723, 36759, 46791, 65535, 140103, 208191, 441027, 4190263, 9056583, 57395631, 172186887, 236923383, 918330183, 3932935775, 4294967295, 4764161215

Offset: 1

Author

N. J. A. Sloane, Mar 13 2004

Keywords

• nonn

Links

• Douglas E. Iannucci, Deng Moujie and Graeme L. Cohen, On Perfect Totient Numbers, J. Integer Seqs., Vol. 6, 2003.

Crossrefs

A082897 has more information.

Programs

Mathematica

fQ[n_] := !IntegerQ@ Log[3, n] && Plus @@ FixedPointList[ EulerPhi@# &, n] == 2n + 1 (* Robert G. Wilson v, Nov 06 2010 *)

Python

from itertools import count, islice
from gmpy2 import digits
from sympy import totient
def A091847_gen(startvalue=3): # generator of terms >= startvalue
    for n in count((k:=max(startvalue,3))+1-(k&1),2):
        t = digits(n,3)
        if t.count('0') != len(t)-1:
            m, s = n, 1
            while (m:=totient(m))>1:
                s += m
            if s == n:
                yield n
A091847_list = list(islice(A091847_gen(),10)) # Chai Wah Wu, Mar 24 2023