A342064 Primes p such that p^8 - 1 has 384 divisors.

821, 997, 2819, 6619, 17827, 20947, 24917, 42709, 43411, 46141, 49261, 51691, 80077, 108803, 158981, 159539, 161341, 171659, 202667, 228611, 268573, 304477, 315803, 350971, 420781, 447683, 463459, 816709, 848227, 887989, 953773, 991811, 1056829, 1131379

Offset: 1

Author

Jon E. Schoenfield, Feb 27 2021

Keywords

• nonn

Comments

Conjecture: sequence is infinite.

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).

Examples

			   p =
n  a(n)               factorization of p^8 - 1
- ----- -----------------------------------------------------
1  821  2^5 * 3 * 5 *  41 *  137 *   337021 *    227165634841
2  997  2^5 * 3 * 5 *  83 *  499 *    99401 *    494026946041
3 2819  2^5 * 3 * 5 *  47 * 1409 *  3973381 *  31575505195561
4 6619  2^5 * 3 * 5 * 331 * 1103 * 21905581 * 959708914083961
		

Crossrefs

Cf. A000005, A000040, A309906, A342062, A342063.

Programs

Mathematica

Select[Prime[Range[90000]],DivisorSigma[0,#^8-1]==384&] (* Harvey P. Dale, Jul 08 2025 *)