A184968 Smallest k such that phi(phi(k)) = 2^n, where phi is the Euler totient function.

5, 11, 17, 41, 85, 137, 257, 641, 1285, 2329, 4369, 10537, 17477, 35209, 65537, 163841, 297109, 557057, 1114129, 2687017, 4491589, 8978569, 16843009, 42009217, 71304257, 143163649, 286331153, 690563369, 1145390149, 2281701377, 4295098369, 10737647617

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Example

a(5) = 85 because phi(85) = 64, phi(64) = 2^5.

Maple

with(numtheory):for n from 1 to 22 do: id:=0:for k from 1 to 10000000 while(id=0)
  do: if phi(phi(k)) =2^n then id:=1:print(k):else fi:od:od:
# Alternative:
f:= proc(n) local S, s, r;
  uses numtheory;
  S:= sort(convert(invphi(2^n), list));
  r:= infinity;
  for s in S while s < r do
    r:= min(r, min(invphi(s)))
  od;
  r
end proc:
map(f, [$1..50]); # Robert Israel, Mar 22 2017

Prog

(PARI) a(n) = {my(v = invphi(2^n), m); for(i = 1, #v, m = invphiMin(v[i]); v[i] = max(m, 0)); vecmin(select(x -> x > 0, v)); } \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000010, A010554.

Sequence in context: A088903 A094205 A136091 * A341357 A022004 A339503

Adjacent sequences: A184965 A184966 A184967 * A184969 A184970 A184971

Keyword

nonn,changed

Author

Michel Lagneau, Mar 27 2011

Extensions

a(23)-a(32) from Donovan Johnson, Jul 28 2011

Status

approved