A318623 a(n) = 2^phi(n) mod n.

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

Author

Jianing Song, Aug 30 2018

Keywords

• nonn
• easy

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).

Examples

			a(6) = 2^phi(6) mod 6 = 2^4 mod 6 = 4.
a(18) = 2^phi(18) mod 18 = 2^6 mod 18 = 10.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A007663, A245970.

Programs

Magma

[Modexp(2, EulerPhi(n), n): n in [1..110]]; // Vincenzo Librandi, Aug 02 2018

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 *)

PARI

a(n) = lift(Mod(2, n)^(eulerphi(n)))

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.