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

1,1

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).

Links

Table of n, a(n) for n=1..34.

Example

   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.

Sequence in context: A230784 A022254 A095964 * A020368 A002140 A095965

Adjacent sequences: A342061 A342062 A342063 * A342065 A342066 A342067

Keyword

nonn

Author

Jon E. Schoenfield, Feb 27 2021

Status

approved