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

Author

Benoit Cloitre, May 06 2002

Keywords

• easy
• nonn

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

Crossrefs

Cf. A069180.

Programs

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 *)

PARI

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

Extensions

More terms from Ralf Stephan, Oct 14 2002