A070174 Primes p such that (p^2)! and 2^(p^2)-1 are not relatively prime.

2, 3, 11, 23, 29, 37, 43, 73, 79, 83, 113, 131, 151, 179, 191, 197, 211, 223, 233, 239, 251, 263, 283, 317, 337, 359, 367, 397, 419, 431, 443, 461, 463, 487, 491, 499, 547, 557, 571, 577, 593, 601, 617, 619, 641, 659, 683, 719

Offset

1,1

Comments

If q is an odd prime (p^2)! and q^(p^2)-1 are not relatively primes for any p prime.

Same as primes p where the smallest prime factor of M(p)=2^p-1 is less than p^2. - William Hu, Aug 18 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(p) local t, q, i;
  if not isprime(p) then return false fi;
  t:= 2^p-1;
  igcd(t, convert(select(isprime, [seq(i, i=1..p^2, 2*p)]), `*`)) <> 1
end proc:
filter(2):= true:
select(filter, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Aug 26 2024

Mathematica

Select[Prime[Range[130]], !CoprimeQ[(#^2)!, 2^#^2-1]&] (* Harvey P. Dale, Jan 15 2022 *)

Prog

(PARI) forprime(n=1, 263, if(gcd((n^2)!, 2^(n^2)-1)>1, print1(n, ", ")))

Crossrefs

Cf. A069180.

Sequence in context: A339753 A236168 A235634 * A372885 A320393 A350853

Adjacent sequences: A070171 A070172 A070173 * A070175 A070176 A070177

Keyword

easy,nonn

Author

Benoit Cloitre, May 06 2002

Extensions

More terms from Ralf Stephan, Oct 14 2002

Status

approved