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 A322568 #32 Sep 21 2019 04:04:13 %S A322568 169,221,323,611,779,793,923,1121,1159,1271,1273,1349,1513,1717,1829, %T A322568 1919,2033,2077,2197,2201,2413,2533,2603,2759,2873,2951,3097,3131, %U A322568 3173,3193,3211,3281,3379,3599,3721,3757,3791,3937,3953,4043,4199,4223,4309,4331 %N A322568 Integers k such that the least prime factor of 2^k - 1 is not in A122094. %C A322568 Clearly, the terms are odd and composite (A071904). %C A322568 The first term which is itself of form 2^j - 1 is 34359738367 = 2^35 - 1. The least prime factor of 2^34359738367 - 1 is 136463, and the multiplicative order of 2 modulo 136463 is 2201 = 31*71. In A309130, it is asked if a member of A322568 can be of form 2^p - 1 with p prime. %e A322568 169 is included because the least prime factor of 2^169-1 is 4057, and the multiplicative order of 2 modulo 4057 is 169 which is not prime. The divisor 4057 is less than the "algebraic" divisor 2^13-1 = 8192 (Mersenne prime). %e A322568 4199 (= 13*17*19) is included because the least prime factor of 2^4199-1 is 647, and the multiplicative order of 2 modulo 647 is 323 (= 17*19) which is not prime. The divisor 647 is less than the smallest "algebraic" divisor which is 2^13-1 = 8192 (Mersenne prime). %e A322568 289 is NOT included; its least prime factor is 2^17 - 1. %e A322568 1073 (= 29*37) is NOT included; its least prime factor is 223, but 223 is a divisor of one of the "algebraic" factors, namely 223 is a divisor of composite Mersenne number 2^37 - 1. %o A322568 (PARI) for(k=2,+oo,isprime(k)&&next();forprime(p=3,,if(Mod(2,p)^k-1==0,!isprime(znorder(Mod(2,p)))&&print1(k,", ");next(2)))) %Y A322568 Cf. A000225, A020639, A122094, A309130. %K A322568 nonn %O A322568 1,1 %A A322568 _Jeppe Stig Nielsen_, Aug 29 2019