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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
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 03 2018
STATUS
approved