A111076 - OEIS

%I #29 Jan 18 2019 08:59:50

%S 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,

%T 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,

%U 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

%N Smallest positive number of maximal order mod n.

%H Charles R Greathouse IV, <a href="/A111076/b111076.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A229708(n) if and only if a(n) is prime. - _Jonathan Sondow_, May 17 2017

%e 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.

%t Table[Min[

%t   Select[Range[n],

%t    CoprimeQ[#, n] &&

%t      MultiplicativeOrder[#, n] == CarmichaelLambda[n] &]], {n, 1, 100}]

%t (* _Geoffrey Critzer_, Jan 04 2015 *)

%o (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

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

%K easy,nonn

%O 1,3

%A _Franklin T. Adams-Watters_, Oct 10 2005