%I #9 Mar 04 2021 01:42:23
%S 821,997,2819,6619,17827,20947,24917,42709,43411,46141,49261,51691,
%T 80077,108803,158981,159539,161341,171659,202667,228611,268573,304477,
%U 315803,350971,420781,447683,463459,816709,848227,887989,953773,991811,1056829,1131379
%N Primes p such that p^8 - 1 has 384 divisors.
%C Conjecture: sequence is infinite.
%C For every term p, p^8 - 1 is of the form 2^5 * 3 * 5 * q * r * s * t, where q, r, s, and t are distinct primes > 5 (see Example section).
%e p =
%e n a(n) factorization of p^8 - 1
%e - ----- -----------------------------------------------------
%e 1 821 2^5 * 3 * 5 * 41 * 137 * 337021 * 227165634841
%e 2 997 2^5 * 3 * 5 * 83 * 499 * 99401 * 494026946041
%e 3 2819 2^5 * 3 * 5 * 47 * 1409 * 3973381 * 31575505195561
%e 4 6619 2^5 * 3 * 5 * 331 * 1103 * 21905581 * 959708914083961
%Y Cf. A000005, A000040, A309906, A342062, A342063.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Feb 27 2021