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 A306270 #28 Sep 25 2020 19:42:10 %S A306270 4,6,12,20,21,28,42,52,60,66,84,105,156,165,186,220,231,273,276,301, %T A306270 364,385,420,465,506,532,561,609,645,651,660,780,804,903,946,1036, %U A306270 1045,1065,1092,1105,1204,1265,1281,1365,1491,1540,1705,1716,1729,1771,1806,1860 %N A306270 Composite numbers k such that b^(k(k-1)) == 1 (mod k^2) for every b coprime to k. %C A306270 These are composites k such that lambda(k^2) divides k(k-1), where lambda is the Carmichael function A002322. %C A306270 Since lambda(p^2) = phi(p^2) = p(p-1), where p is a prime, then by Euler's theorem b^(p(p-1)) == 1 (mod p^2) for every b indivisible by p. %C A306270 This sequence includes all Carmichael numbers A002997. %C A306270 Conjecture: all semiprimes > 4 in this sequence are in A190275. - _Thomas Ordowski_, Jul 19 2020 %C A306270 The conjecture was verified up to 1063290841. - _Amiram Eldar_, Jul 19 2020 %t A306270 Select[Range[2000], CompositeQ[#] && Divisible[#(#-1), CarmichaelLambda[#^2]] &] %o A306270 (PARI) isok(k) = (k!=1) && !isprime(k) && !(k*(k-1) % lcm(znstar(k^2)[2])); \\ _Michel Marcus_, Mar 12 2019 %Y A306270 Cf. A002322, A002997, A306259. %Y A306270 A190275 is a subsequence. - _Thomas Ordowski_, Jul 19 2020 %K A306270 nonn %O A306270 1,1 %A A306270 _Amiram Eldar_ and _Thomas Ordowski_, Feb 01 2019