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A318262 Numbers m such that 2^phi(m) mod m is a prime power (in the sense of A246655). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)