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%I #17 Jun 05 2021 17:26:05
%S 31,43,109,127,151,157,223,229,241,251,277,283,307,331,397,431,433,
%T 439,457,499,571,601,631,641,643,673,683,691,727,733,739,811,911,919,
%U 953,971,997,1013,1021,1051,1069,1093,1103,1163,1181,1321,1327,1399,1423,1429
%N Primes p such that the order of 2 modulo p is not divisible by the largest odd divisor of p - 1.
%C Every prime factor of a composite Fermat number belongs to this sequence.
%C If a prime of the form 3*2^k + 1 belongs to this sequence, then k is in A204620 (see Golomb).
%C Primes p such that A014664(primepi(p)) is not divisible by A057023(primepi(p)). - _Michel Marcus_, Apr 26 2021
%H Solomon W. Golomb, <a href="https://doi.org/10.1090/S0025-5718-1976-0404129-8">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663.
%t Select[Prime@Range@300,Mod[MultiplicativeOrder[2,#],Max@Select[Divisors[#-1],OddQ]]!=0&] (* _Giorgos Kalogeropoulos_, Apr 02 2021 *)
%o (PARI) forprime(p=3, 1429, if(Mod(znorder(Mod(2, p)), (p-1)>>valuation(p-1, 2)), print1(p, ", ")));
%Y Cf. A014664, A023394, A057023, A204620, A226366, A280003, A280004.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Apr 01 2021