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%I #6 Mar 07 2021 01:05:34
%S 3,467,2039,4679,5399,5939,6899,8783,12347,16487,18443,23879,25583,
%T 33647,35879,36299,44819,47207,53147,57119,67499,74507,90239,93287,
%U 96059,119759,125003,133499,135119,136223,157019,159539,164999,165059,168887,178799,188159
%N Primes p such that p^11 - 1 has 8 divisors.
%C Conjecture: sequence is infinite.
%C The only primes p such that p^11 - 1 has fewer than A309906(11)=8 divisors are 2 and 5.
%C p^11 - 1 = (p-1)*(p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1).
%C For every term p, p^11 - 1 is of the form 2*q*r, where q and r are distinct odd primes. With the exception of p=a(1)=3, each term p is a number such that (p-1)/2 and (p^10 + p^9 + p^8 + ... + p^2 + p + 1) are primes.
%e p =
%e n a(n) factorization of p^11 - 1
%e - ---- ------------------------------------------------
%e 1 3 2 * 23 * 3851
%e 2 467 2 * 233 * 494424256962371823779424877
%e 3 2039 2 * 1019 * 1242754384106847037173120489949801
%e 4 4679 2 * 2339 * 5030640462820574591105701447273296601
%o (PARI) isok(p) = isprime(p) && (numdiv(p^11-1) == 8); \\ _Michel Marcus_, Feb 28 2021
%Y Cf. A000005, A000040, A309906, A341670.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Feb 28 2021
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