OFFSET
1,1
COMMENTS
EXAMPLE
10 is an infinitary perfect totient number because iphi(10) + iphi(iphi(10)) + ... = 4 + 3 + 2 + 1 = 10.
MATHEMATICA
f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); infPerfTotQ[n_] := Plus @@ FixedPointList[iphi@# &, n] == 2 n + 1; Select[Range[1000], infPerfTotQ]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Dec 13 2019
STATUS
approved