A340762 Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 4, 2, 1.

4, 5, 8, 10, 11, 12, 13, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset

1,1

Comments

Infinite set (see reference).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eliot T. Jacobson and Alan E. Parks, Infinite branches of the phi-tree, Amer. Math. Monthly, Vol. 93, No. 7 (August-September 1986), pp. 552-554.

Keith Matthews, Solving phi(x)=n, where phi(x) is Euler's totient function.

Example

11 is in the list because phi(phi(11)))) = phi(10) = 4.

Maple

filter:= proc(n) option remember;
  if n < 4 then false
  elif n = 4 then true
  else procname(numtheory:-phi(n))
  fi
end proc:
select(filter, [$4..100]); # Robert Israel, Dec 23 2021

Mathematica

Select[Range[4, 72], FixedPointList[EulerPhi, #][[-4]] == 4 &] (* Amiram Eldar, Jan 27 2021 *)

Prog

(PARI) isok(k) = if (k>=4, while((k!=6) && (k!=4), k=eulerphi(k))); k == 4; \\ Michel Marcus, Feb 01 2021

Crossrefs

Cf. A000010, A340765 (complement relative to {n>=4}).

Cf. A003434, A032358, A049108.

Sequence in context: A064394 A346457 A141220 * A092022 A346302 A190200

Adjacent sequences: A340759 A340760 A340761 * A340763 A340764 A340765

Keyword

nonn

Author

Franz Vrabec, Jan 20 2021

Status

approved