%I #8 Sep 11 2021 10:47:55
%S 2,2,2,0,2,2,3,2,0,3,2,2,3,3,2,0,2,2,3,2,2,269,3,3,0,2,2,7,5,29,11,2,
%T 2,3,2,0,11,2,5,3,2,2,5,3,2,5,5,2,0,2,17,3,2,11,3,2,2,3,7,2,7,5,2,0,3,
%U 2,3,2,5,7,2,3,5,3,3,5,2,2,3,3,0,41,2,3,7,7,2,3,3,2,5,2,3,53,2,2,3,3,7,0
%N a(n) is the least prime p such that n*(p#^2)-1 is prime or 0 if n > 1 is a square so no prime possible.
%e 1*(2^2)-1 = 3 is prime, so a(1) = 2.
%e 7*(2^2)-1 = 27 is composite, 7*((2*3)^2)-1 = 251 is prime, so a(7) = 3.
%t a[n_] := If[n>1 && IntegerQ[Sqrt[n]], 0, Module[{p = pr = 2}, While[!PrimeQ[n * pr^2 - 1], p = NextPrime[p]; pr *= p]; p]]; Array[a, 100] (* _Amiram Eldar_, Sep 11 2021 *)
%K nonn
%O 1,1
%A _Pierre CAMI_, May 19 2006