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A318145
Numbers m such that 2^phi(m) mod m is a perfect power other than 1.
2
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 01 2018
EXTENSIONS
Definition corrected by Robert Israel, Sep 02 2018
STATUS
approved