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A318623
a(n) = 2^phi(n) mod n.
3
0, 0, 1, 0, 1, 4, 1, 0, 1, 6, 1, 4, 1, 8, 1, 0, 1, 10, 1, 16, 1, 12, 1, 16, 1, 14, 1, 8, 1, 16, 1, 0, 1, 18, 1, 28, 1, 20, 1, 16, 1, 22, 1, 12, 1, 24, 1, 16, 1, 26, 1, 40, 1, 28, 1, 8, 1, 30, 1, 16, 1, 32, 1, 0, 1, 34, 1, 52, 1, 36, 1, 64, 1, 38, 1, 20, 1, 40, 1
OFFSET
1,6
COMMENTS
Of course, a(n) = 0 iff n is a power of 2 and a(n) = 1 iff n is an odd number > 1. For other n, let n = 2^t*s, t > 0, s > 1 is an odd number, then a(n) is the unique solution to x == 0 (mod 2^t) and x == 1 (mod s).
LINKS
FORMULA
If n is a power of 2 then a(n) = 0; if n is an odd number > 1 then a(n) = 1; else, let n = 2^t*s, t > 0, s > 1 is an odd number, then a(n) = n - (s mod 2^t)^2 + 1.
EXAMPLE
a(6) = 2^phi(6) mod 6 = 2^4 mod 6 = 4.
a(18) = 2^phi(18) mod 18 = 2^6 mod 18 = 10.
MATHEMATICA
a[n_] = Mod[2^EulerPhi[n], n]; Array[a, 50] (* Stefano Spezia, Sep 01 2018 *)
Table[PowerMod[2, EulerPhi[n], n], {n, 80}] (* Harvey P. Dale, Nov 07 2021 *)
PROG
(PARI) a(n) = lift(Mod(2, n)^(eulerphi(n)))
(Magma) [Modexp(2, EulerPhi(n), n): n in [1..110]]; // Vincenzo Librandi, Aug 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Aug 30 2018
STATUS
approved