

A111076


Smallest positive number of maximal order mod n.


9



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
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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(n1)); 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: A064886 A029600 A169616 * A162398 A131470 A255709
Adjacent sequences: A111073 A111074 A111075 * A111077 A111078 A111079


KEYWORD

easy,nonn


AUTHOR

Franklin T. AdamsWatters, Oct 10 2005


STATUS

approved



