A318145 Numbers m such that 2^phi(m) mod m is a perfect power other than 1.

6, 12, 14, 20, 24, 28, 30, 40, 48, 56, 60, 62, 70, 72, 80, 84, 96, 112, 120, 124, 126, 132, 140, 144, 168, 176, 192, 198, 208, 224, 240, 248, 252, 254, 260, 272, 286, 288, 320, 336, 340, 344, 384, 390, 396, 408, 430, 448, 456, 480, 496, 504, 508, 510, 532

Offset

1,1

Comments

All terms are even, as 2^phi(m) == 1 (mod m) if m is odd. - Robert Israel, Sep 02 2018

Perfect power terms are 144, 576, 900, 1600, 3136, 9216, 12544, 20736, 36864, 57600, 63504, ... - Altug Alkan, Sep 04 2018

Links

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

Maple

ispow:= proc(n) local F;
  F:= map(t -> t[2], ifactors(n)[2]);
  igcd(op(F)) > 1
end proc:
select(m -> ispow(2 &^ numtheory:-phi(m) mod m), [seq(i, i=2..1000, 2)]); # Robert Israel, Sep 02 2018

Mathematica

okQ[n_] := GCD @@ FactorInteger[PowerMod[2, EulerPhi[n], n]][[All, 2]] > 1;
Select[Range[2, 1000, 2], okQ] (* Jean-François Alcover, Aug 02 2019 *)

Prog

(Sage)
def isA318145(n):
    m = power_mod(2, euler_phi(n), n)
    return m > 0 and m.is_perfect_power()
def A318145_list(search_bound):
    return [n for n in range(2, search_bound + 1, 2) if isA318145(n)]
print(A318145_list(532))

Crossrefs

Cf. A000010, A001597, A318623. Contains A139257.

Sequence in context: A031405 A315602 A315603 * A318262 A315604 A315605

Adjacent sequences: A318142 A318143 A318144 * A318146 A318147 A318148

Keyword

nonn

Author

Peter Luschny, Sep 01 2018

Extensions

Definition corrected by Robert Israel, Sep 02 2018

Status

approved