A111076 Smallest positive number of maximal order mod n.

1, 1, 2, 3, 2, 5, 3, 3, 2, 3, 2, 5, 2, 3, 2, 3, 3, 5, 2, 3, 2, 7, 5, 5, 2, 7, 2, 3, 2, 7, 3, 3, 2, 3, 2, 5, 2, 3, 2, 3, 6, 5, 3, 3, 2, 5, 5, 5, 3, 3, 5, 7, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 7, 5, 5, 5, 2, 3, 2, 7, 3, 3, 2, 7, 2, 5, 3, 3, 2, 3, 3, 7, 2, 3, 11, 5, 2, 5, 5, 3, 2, 3

Offset

1,3

Links

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

Formula

a(n) = A229708(n) if and only if a(n) is prime. - Jonathan Sondow, May 17 2017

Example

a(6)=5 because order of 1 is 1 and 2 through 4 are not relatively prime to 6, but 5 has order 2, which is the maximum possible.

Mathematica

Table[Min[
  Select[Range[n],
   CoprimeQ[#, n] &&
     MultiplicativeOrder[#, n] == CarmichaelLambda[n] &]], {n, 1, 100}]
(* Geoffrey Critzer, Jan 04 2015 *)

Prog

(PARI) a(n)=if(n==1, return(1)); if(n<5, return(n-1)); my(o=lcm(znstar(n)[2]), k=1); while(gcd(k++, n)>1 || znorder(Mod(k, n))<o, ); k \\ Charles R Greathouse IV, Jul 31 2013

Crossrefs

Cf. A002322 (orders); same as A046145 for n with primitive roots; see also A001918 (for primes), A229708.

Sequence in context: A029600 A169616 A344448 * A361624 A162398 A131470

Adjacent sequences: A111073 A111074 A111075 * A111077 A111078 A111079

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Oct 10 2005

Status

approved