This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342064 #11 Jul 08 2025 11:02:51 %S A342064 821,997,2819,6619,17827,20947,24917,42709,43411,46141,49261,51691, %T A342064 80077,108803,158981,159539,161341,171659,202667,228611,268573,304477, %U A342064 315803,350971,420781,447683,463459,816709,848227,887989,953773,991811,1056829,1131379 %N A342064 Primes p such that p^8 - 1 has 384 divisors. %C A342064 Conjecture: sequence is infinite. %C A342064 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 A342064 p = %e A342064 n a(n) factorization of p^8 - 1 %e A342064 - ----- ----------------------------------------------------- %e A342064 1 821 2^5 * 3 * 5 * 41 * 137 * 337021 * 227165634841 %e A342064 2 997 2^5 * 3 * 5 * 83 * 499 * 99401 * 494026946041 %e A342064 3 2819 2^5 * 3 * 5 * 47 * 1409 * 3973381 * 31575505195561 %e A342064 4 6619 2^5 * 3 * 5 * 331 * 1103 * 21905581 * 959708914083961 %t A342064 Select[Prime[Range[90000]],DivisorSigma[0,#^8-1]==384&] (* _Harvey P. Dale_, Jul 08 2025 *) %Y A342064 Cf. A000005, A000040, A309906, A342062, A342063. %K A342064 nonn %O A342064 1,1 %A A342064 _Jon E. Schoenfield_, Feb 27 2021