This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368042 #15 Feb 05 2024 11:24:16 %S A368042 2,24,40,48,56,60,63,65,72,80,84,85,88,91,96,104,105,112,117,120,126, %T A368042 130,132,133,136,140,144,145,152,156,160,165,168,170,171,176,180,182, %U A368042 184,185,189,192,195,200,204,205,208,210,216,217 %N A368042 Moduli k for which the number of quadratic residues mod k coprime to k is phi(k)/2^r for positive r = (phi(k)/lambda(k)) - x, x > 0, where lambda is Carmichael's function. Complement of A366935. %C A368042 An empirical observation, verified for 2 <= k <= 10^5: The number of quadratic residues mod k coprime to k is |Q_k| = phi(k)/2^r, r = A046072(k) <= phi(k)/lambda(k). Up to 10^5, the equality holds for 37758 moduli, and the inequality holds for 62241. %D A368042 D. Shanks, Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993, page 95. %e A368042 k = 2 is a term: |Q_2| = phi(2)/2^0 = 1, and r = 0 < phi(2)/lambda(2) = 1. %o A368042 (PARI) isok(n) = my(z=znstar(n).cyc); #z < eulerphi(n)/lcm(z) %Y A368042 Cf. A366935, A000010, A002322, A046073, A034380, A033948, A046072. %K A368042 nonn,easy %O A368042 1,1 %A A368042 _Miles Englezou_, Dec 09 2023