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A342064 Primes p such that p^8 - 1 has 384 divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)