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

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

Example

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,

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A315602 A315603 A318145 * A315604 A315605 A315606

Adjacent sequences: A318259 A318260 A318261 * A318263 A318264 A318265

Keyword

nonn

Author

Peter Luschny, Sep 03 2018

Status

approved