A215486 n - 1 mod phi(n), where phi(n) is Euler's totient function.

0, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 3, 0, 1, 6, 7, 0, 5, 0, 3, 8, 1, 0, 7, 4, 1, 8, 3, 0, 5, 0, 15, 12, 1, 10, 11, 0, 1, 14, 7, 0, 5, 0, 3, 20, 1, 0, 15, 6, 9, 18, 3, 0, 17, 14, 7, 20, 1, 0, 11, 0, 1, 26, 31, 16, 5, 0, 3, 24, 21, 0, 23, 0, 1, 34, 3, 16, 5, 0, 15, 26, 1, 0, 11, 20, 1, 30, 7, 0, 17

Offset: 1

Author

Alonso del Arte, Feb 17 2013, based on an idea from Balarka Sen

Keywords

• nonn
• easy

Comments

Lehmer conjectured that a(n) = 0 only when n is 1 or prime.

Examples

			a(8) = 3 because 8 - 1 mod phi(8) = 3.
a(9) = 2 because 9 - 1 mod phi(9) = 2.
a(10) = 1 because 10 - 1 mod phi(10) = 1.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Wikipedia, Lehmer's totient problem

Crossrefs

Cf. A068494, A007694.

Programs

Magma

[(n-1) mod EulerPhi(n): n in [2..90]]; // Bruno Berselli, Feb 18 2013

Mathematica

Table[Mod[n - 1, EulerPhi[n]], {n, 2, 100}]

Maxima

makelist(mod(n-1,totient(n)), n, 2, 90); /* Bruno Berselli, Feb 18 2013 */

PARI

a(n)=(n-1)%eulerphi(n) \\ Charles R Greathouse IV, Dec 29 2013