OFFSET
1,1
COMMENTS
Clearly, the terms are odd and composite (A071904).
EXAMPLE
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).
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).
289 is NOT included; its least prime factor is 2^17 - 1.
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.
PROG
(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))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Aug 29 2019
STATUS
approved