A354183 Primes p such that p divides 2^((p-1)/x) - 1, where x is the greatest prime factor of p - 1.

17, 109, 151, 241, 251, 257, 331, 433, 631, 641, 673, 683, 1321, 1429, 1459, 1613, 2917, 3191, 3457, 3889, 4733, 4861, 5153, 5419, 6337, 7001, 7351, 8581, 9719, 11119, 11251, 11471, 12101, 13367, 13553, 13669, 14323, 14449, 15121, 17539, 18503, 20231, 20857

Offset: 1

Author

Arkadiusz Wesolowski, May 18 2022

Keywords

• nonn

Comments

Together with 3 and 5, supersequence of A023394.

Are there any odd integers k (k is not a Sierpiński number) such that every prime of the form k*2^m + 1 (m >= 1) does not belong to the sequence?

Crossrefs

Cf. A023394.

Programs

Magma

gpf:=func; [p: p in PrimesUpTo(20857) | Modexp(2, Truncate((p-1)/gpf(p-1)), p) eq 1];

Mathematica

Select[Prime[Range[2500]], PowerMod[2, (# - 1)/FactorInteger[# - 1][[-1, 1]], #] == 1 &] (* Amiram Eldar, May 19 2022 *)

PARI

isok(p) = if (isprime(p) && (p>2), my(x=vecmax(factor(p-1)[,1])); ((2^((p-1)/x) - 1) % p) == 0); \\ Michel Marcus, May 19 2022