cp's OEIS Frontend

A318262 Numbers m such that 2^phi(m) mod m is a prime power (in the sense of A246655).

%I A318262 #33 Mar 14 2020 05:37:45
%S A318262 6,12,14,20,24,28,30,40,48,56,60,62,72,80,84,96,112,120,124,126,144,
%T A318262 168,192,224,240,248,252,254,272,288,320,336,340,384,408,448,480,496,
%U A318262 504,508,510,544,576,584,640,672,680,768,816,896,960,992,1008,1016,1020
%N A318262 Numbers m such that 2^phi(m) mod m is a prime power (in the sense of A246655).
%C A318262 m is in this sequence if and only if 2^phi(m) mod m = 2^k for some k > 0.
%C A318262 There is no prime power in this sequence. Perfect power terms of this sequence are 144, 576, 9216, 36864, 589824, 884736, 1638400, 2359296, 3211264, 6553600, 7077888, ... - _Altug Alkan_, Sep 04 2018
%e A318262 The odd part of the first few terms can be arranged as follows:
%e A318262 3,
%e A318262 3, 7,                         5,
%e A318262 3, 7, 15,                     5,
%e A318262 3, 7, 15, 31,              9, 5, 21,
%e A318262 3, 7, 15, 31, 63,          9,    21,
%e A318262 3, 7, 15, 31, 63, 127, 17, 9, 5, 21, 85,
%t A318262 Select[Range[2^10], And[PrimePowerQ@ #, ! PrimeQ@ #] &@ Mod[2^EulerPhi@ #, #] &] (* _Michael De Vlieger_, Sep 04 2018 *)
%o A318262 (Sage)
%o A318262 def isA318262(n):
%o A318262     m = power_mod(2, euler_phi(n), n)
%o A318262     return m.is_prime_power()
%o A318262 def A318262_list(search_bound):
%o A318262     return [n for n in range(2,search_bound+1,2) if isA318262(n)]
%o A318262 print(A318262_list(1020))
%o A318262 (PARI) isok(n) = isprimepower(lift(Mod(2, n)^eulerphi(n))); \\ _Michel Marcus_, Sep 06 2018
%Y A318262 Cf. A000010, A001597, A118372, A246655, A292544, A318623, A318145.
%K A318262 nonn
%O A318262 1,1
%A A318262 _Peter Luschny_, Sep 03 2018