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A341666 Primes p such that p^6 - 1 has 384 divisors.

%I A341666 #14 Mar 04 2021 01:43:09
%S A341666 29,43,59,83,157,193,317,1093,1373,1523,2803,3557,3677,3733,12227,
%T A341666 13093,20507,25933,28163,29243,32443,33493,38603,53917,100523,109883,
%U A341666 122117,134363,140197,190573,236723,242773,249397,256757,258403,274237,299723,333283
%N A341666 Primes p such that p^6 - 1 has 384 divisors.
%C A341666 Conjecture: sequence is infinite.
%C A341666 For every term p, p^6 - 1 is of the form 2^3 * 3^2 * 7 * q * r * s * t, where q, r, s, and t are distinct primes > 7, with four exceptions: p = 29, 59, 193, and 1373 (see Example section).
%e A341666   p =
%e A341666 n a(n)                factorization of p^6 - 1
%e A341666 - ---- ------------------------------------------------------
%e A341666 1   29 2^3 * 3^2 * 5 * 7   *  13 *     67 *     271
%e A341666 2   43 2^3 * 3^2     * 7   *  11 *     13 *     139 *     631
%e A341666 3   59 2^3 * 3^2 * 5 * 7   *  29 *    163 *    3541
%e A341666 4   83 2^3 * 3^2     * 7   *  19 *     41 *     367 *    2269
%e A341666 5  157 2^3 * 3^2     * 7   *  13 *     79 *    3499 *    8269
%e A341666 6  193 2^7 * 3^2     * 7   *  97 *   1783 *   37057
%e A341666 7  317 2^3 * 3^2     * 7   *  53 *     79 *   14401 *   33391
%e A341666 8 1093 2^3 * 3^2     * 7   *  13 *    547 *  398581 * 1193557
%e A341666 9 1373 2^3 * 3^2     * 7^3 * 229 * 627919 * 1886503
%t A341666 Select[Range[350000], PrimeQ[#] && DivisorSigma[0, #^6 - 1] == 384 &] (* _Amiram Eldar_, Feb 27 2021 *)
%o A341666 (PARI) isok(p) = isprime(p) && (numdiv(p^6-1) == 384); \\ _Michel Marcus_, Feb 27 2021
%Y A341666 Cf. A000005, A000040, A309906, A341657, A341667.
%K A341666 nonn
%O A341666 1,1
%A A341666 _Jon E. Schoenfield_, Feb 26 2021