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

1,1

Links

Table of n, a(n) for n=1..30.

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

Mathematica

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

Prog

(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

Crossrefs

A082897 has more information.

Sequence in context: A186295 A259429 A126950 * A062222 A369720 A369758

Adjacent sequences: A091844 A091845 A091846 * A091848 A091849 A091850

Keyword

nonn

Author

N. J. A. Sloane, Mar 13 2004

Status

approved