A350179 Primes of the form ( A349309(n) + 1 ) ^ (1/3).

2, 3, 5, 7, 11, 13, 23, 29, 31, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 131, 139, 149, 151, 157, 167, 173, 179, 191, 197, 211, 223, 227, 229, 239, 263, 269, 277, 283, 293, 311, 317, 331, 347, 349, 359, 367, 373, 383, 389, 419, 421, 431, 439, 443, 461, 463, 467

Offset: 1

Author

Flávio V. Fernandes, Dec 23 2021

Keywords

• nonn

Comments

Equivalently, primes p such that A051903(p^3-1) < 3. - Amiram Eldar, Dec 26 2021

Examples

			5 is a term since (A349309(3) + 1) ^ (1/3) = 125 ^ (1/3) = 5.
		

Crossrefs

Cf. A051903, A349309.

Programs

Maple

filter:= n -> isprime(n) and max(map(t -> t[2],ifactors(n^3-1)[2]))<3:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Dec 26 2021

Mathematica

q[p_] := PrimeQ[p] && AllTrue[FactorInteger[p^3 - 1][[;; , 2]], # < 3 &]; Select[Range[500], q] (* Amiram Eldar, Dec 26 2021 *)

PARI

isok(p) = isprime(p) && (vecmax(factor(p^3-1)[,2]) < 3); \\ Michel Marcus, Jul 18 2022

Python

from itertools import count, islice
from sympy import prime, factorint
def A350179_gen(): return (p for p in (prime(n) for n in count(1)) if max(factorint(p**3-1).values()) < 3)
A350179_list = list(islice(A350179_gen(),30)) # Chai Wah Wu, Jan 24 2022

Extensions

More terms from Michel Marcus, Dec 25 2021