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A277777 Largest nontrivial square root of unity modulo the n-th positive integer that does not have a primitive root (A033949).

%I A277777 #26 Oct 26 2022 13:12:24
%S A277777 5,7,11,9,11,13,19,15,19,17,23,29,19,25,31,29,23,26,41,35,27,34,43,37,
%T A277777 49,55,33,51,43,35,47,41,55,49,39,43,53,71,71,69,59,67,71,64,47,61,56,
%U A277777 79,89,51,67,79,76,55,89,73,97,77,91,59,64,69,109,83,63,71
%N A277777 Largest nontrivial square root of unity modulo the n-th positive integer that does not have a primitive root (A033949).
%H A277777 Alois P. Heinz, <a href="/A277777/b277777.txt">Table of n, a(n) for n = 1..10000</a>
%H A277777 Wikipedia, <a href="https://en.wikipedia.org/wiki/Root_of_unity_modulo_n">Root of unity modulo n</a>
%F A277777 a(n) = A033949(n) - A082568(n).
%o A277777 (Python)
%o A277777 from gmpy2 import *
%o A277777 def f(n):
%o A277777   for k in range(n - 2, 0, -1):
%o A277777     if pow(k, 2, n) == 1:
%o A277777       return k
%o A277777 def A277777(L):
%o A277777   return [j for j in [f(k) for k in range(3, L + 1)] if j > 1] # _Darío Clavijo_, Oct 15 2022
%o A277777 (Python)
%o A277777 from itertools import count, islice
%o A277777 from sympy.ntheory import sqrt_mod_iter
%o A277777 def A277777_gen(): # generator of terms
%o A277777     for n in count(3):
%o A277777         if (m:=max(filter(lambda k:k<n-1,sqrt_mod_iter(1,n)))) > 1:
%o A277777             yield m
%o A277777 A277777_list = list(islice(A277777_gen(),30)) # _Chai Wah Wu_, Oct 26 2022
%Y A277777 Last elements of nonempty rows of A277776.
%Y A277777 Cf. A033948, A033949, A082568.
%K A277777 nonn,look
%O A277777 1,1
%A A277777 _Alois P. Heinz_, Oct 30 2016