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Primes p such that p^8 - 1 has 384 divisors.
2

%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