A318145 -id:A318145 - cp's OEIS frontend

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

6, 12, 14, 20, 24, 28, 30, 40, 48, 56, 60, 62, 72, 80, 84, 96, 112, 120, 124, 126, 144, 168, 192, 224, 240, 248, 252, 254, 272, 288, 320, 336, 340, 384, 408, 448, 480, 496, 504, 508, 510, 544, 576, 584, 640, 672, 680, 768, 816, 896, 960, 992, 1008, 1016, 1020

Offset: 1

Peter Luschny, Sep 03 2018

nonn

m is in this sequence if and only if 2^phi(m) mod m = 2^k for some k > 0.

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

			The odd part of the first few terms can be arranged as follows:
3,
3, 7,                         5,
3, 7, 15,                     5,
3, 7, 15, 31,              9, 5, 21,
3, 7, 15, 31, 63,          9,    21,
3, 7, 15, 31, 63, 127, 17, 9, 5, 21, 85,

Cf. A000010, A001597, A118372, A246655, A292544, A318623, A318145.

Select[Range[2^10], And[PrimePowerQ@ #, ! PrimeQ@ #] &@ Mod[2^EulerPhi@ #, #] &] (* Michael De Vlieger, Sep 04 2018 *)

isok(n) = isprimepower(lift(Mod(2, n)^eulerphi(n))); \\ Michel Marcus, Sep 06 2018

def isA318262(n):
    m = power_mod(2, euler_phi(n), n)
    return m.is_prime_power()
def A318262_list(search_bound):
    return [n for n in range(2,search_bound+1,2) if isA318262(n)]
print(A318262_list(1020))

cp's OEIS Frontend

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

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