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

%I A070174 #21 Aug 28 2024 11:33:12
%S A070174 2,3,11,23,29,37,43,73,79,83,113,131,151,179,191,197,211,223,233,239,
%T A070174 251,263,283,317,337,359,367,397,419,431,443,461,463,487,491,499,547,
%U A070174 557,571,577,593,601,617,619,641,659,683,719
%N A070174 Primes p such that (p^2)! and 2^(p^2)-1 are not relatively prime.
%C A070174 If q is an odd prime (p^2)! and q^(p^2)-1 are not relatively primes for any p prime.
%C A070174 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
%H A070174 Robert Israel, <a href="/A070174/b070174.txt">Table of n, a(n) for n = 1..10000</a>
%p A070174 filter:= proc(p) local t,q,i;
%p A070174   if not isprime(p) then return false fi;
%p A070174   t:= 2^p-1;
%p A070174   igcd(t, convert(select(isprime,[seq(i,i=1..p^2,2*p)]),`*`)) <> 1
%p A070174 end proc:
%p A070174 filter(2):= true:
%p A070174 select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Aug 26 2024
%t A070174 Select[Prime[Range[130]],!CoprimeQ[(#^2)!,2^#^2-1]&] (* _Harvey P. Dale_, Jan 15 2022 *)
%o A070174 (PARI) forprime(n=1,263,if(gcd((n^2)!,2^(n^2)-1)>1,print1(n,",")))
%Y A070174 Cf. A069180.
%K A070174 easy,nonn
%O A070174 1,1
%A A070174 _Benoit Cloitre_, May 06 2002
%E A070174 More terms from _Ralf Stephan_, Oct 14 2002