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

1,8

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Wikipedia, Lehmer's totient problem

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A068494, A007694.

Sequence in context: A355340 A275327 A359677 * A083721 A158459 A319666

Adjacent sequences: A215483 A215484 A215485 * A215487 A215488 A215489

Keyword

nonn,easy

Author

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

Status

approved