A219175 a(n) = n mod lambda(n) where lambda is the Carmichael function (A002322).

0, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 1, 0, 1, 0, 3, 2, 1, 0, 5, 2, 9, 4, 1, 2, 1, 0, 3, 2, 11, 0, 1, 2, 3, 0, 1, 0, 1, 4, 9, 2, 1, 0, 7, 10, 3, 4, 1, 0, 15, 2, 3, 2, 1, 0, 1, 2, 3, 0, 5, 6, 1, 4, 3, 10, 1, 0, 1, 2, 15, 4, 17, 6, 1, 0, 27, 2, 1, 0, 5

Offset: 1

Author

Michel Lagneau, Nov 13 2012

Keywords

• nonn

Comments

a(n) = A068494(n) for n = 1..14.

a(k) = 1 for k = prime(n) > 2 or k = A002997(n).

a(n) is the smallest k >= 0 such that b^(n-k) == 1 (mod n) for every b coprime to n. - Thomas Ordowski, Jun 30 2017

Examples

			a(9) = 3 because lambda(9) = 6 and 9 == 3 mod 6.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068494, A002322, A002997.

Programs

Maple

with(numtheory):for n from 1 to 100 do: x:=irem(n,lambda(n)): printf(`%d, `,x):od:

Mathematica

Table[Mod[n, CarmichaelLambda[n]], {n, 100}] (* T. D. Noe, Nov 13 2012 *)

PARI

a(n)=n%lcm(znstar(n)[2]) \\ Charles R Greathouse IV, Nov 13 2012