A377939 - OEIS

%I #6 Nov 11 2024 22:26:20

%S 3,5,7,17,19,22,23,29,31,33,37,43,47,53,55,71,85,87,89,91,102,103,105,

%T 106,109,111,112,113,115,116,117,122,123,133,139,141,143,145,149,153,

%U 155,157,162,163,167,175,177,191,193,199,201,203,209,211,221,223,233,239,241,243,245,247,249,253

%N Nonsquares k such that A377938(k) is not a prime.

%C Numbers k such that k is a primitive root modulo some nonprime x > k but not modulo any prime between k and x.

%C Numbers k such that 0 < A377938(k) < A023049(k).

%H Robert Israel, <a href="/A377939/b377939.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 7 is a term because 7 is a primitive root mod 10, while the least prime > 7 for which 7 is a primitive root is 11.

%p filter:= proc(n) local k;

%p   if issqr(n) then return false fi;

%p   for k from n+1 do

%p     if igcd(k,n) = 1 and numtheory:-order(n,k) = numtheory:-phi(k) then return not isprime(k) fi

%p   od

%p end proc:

%p select(filter, [$2..1000]);

%Y Cf. A023049, A377938.

%K nonn

%O 1,1

%A _Robert Israel_, Nov 11 2024