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%I #24 Mar 13 2020 16:59:42
%S 6,12,14,20,24,28,30,40,48,56,60,62,70,72,80,84,96,112,120,124,126,
%T 132,140,144,168,176,192,198,208,224,240,248,252,254,260,272,286,288,
%U 320,336,340,344,384,390,396,408,430,448,456,480,496,504,508,510,532
%N Numbers m such that 2^phi(m) mod m is a perfect power other than 1.
%C All terms are even, as 2^phi(m) == 1 (mod m) if m is odd. - _Robert Israel_, Sep 02 2018
%C Perfect power terms are 144, 576, 900, 1600, 3136, 9216, 12544, 20736, 36864, 57600, 63504, ... - _Altug Alkan_, Sep 04 2018
%H Robert Israel, <a href="/A318145/b318145.txt">Table of n, a(n) for n = 1..10000</a>
%p ispow:= proc(n) local F;
%p F:= map(t -> t[2], ifactors(n)[2]);
%p igcd(op(F)) > 1
%p end proc:
%p select(m -> ispow(2 &^ numtheory:-phi(m) mod m), [seq(i,i=2..1000,2)]); # _Robert Israel_, Sep 02 2018
%t okQ[n_] := GCD @@ FactorInteger[PowerMod[2, EulerPhi[n], n]][[All, 2]] > 1;
%t Select[Range[2, 1000, 2], okQ] (* _Jean-François Alcover_, Aug 02 2019 *)
%o (Sage)
%o def isA318145(n):
%o m = power_mod(2, euler_phi(n), n)
%o return m > 0 and m.is_perfect_power()
%o def A318145_list(search_bound):
%o return [n for n in range(2, search_bound + 1, 2) if isA318145(n)]
%o print(A318145_list(532))
%Y Cf. A000010, A001597, A318623. Contains A139257.
%K nonn
%O 1,1
%A _Peter Luschny_, Sep 01 2018
%E Definition corrected by _Robert Israel_, Sep 02 2018
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