%I #5 Mar 30 2012 18:35:55

%S 1,3,13,47,463,25683,4187997

%N a(1) = 1 ; for n > 1, a(n) is the smallest number such that a(n)^2 + 1 contains n distinct prime divisors dividing a(n+1)^2 + 1.

%C This sequence is not the same as A180278.

%e a(1) = 1^1 + 1 = 2 ;

%e a(2) = 3^2 + 1 = 2*5 ;

%e a(3) = 13^2 + 1 = 2*5*17 ;

%e a(4) = 47^2 + 1 = 2*5*13*17 ;

%e a(5) = 463^2 + 1 = 2*5*13*17*97 ;

%e a(6) = 25683^2 + 1 = 2 * 5 * 13 * 17 ^ 2 * 97 * 181 ;

%e a(7) = 4187997^2 + 1 = 2 * 5 * 13 * 17 * 97 * 181 * 452033.

%p with(numtheory):A:={2}:for n from 1 to 7 do:id:=0:for k from 1 to 4200000 (id=0) do:x:=k^2+1:y:=factorset(x):n1:=nops(y):if n1=n and A intersect y = A then A:=y:id:=1:printf ( "%d %d \n",n,k):else fi:od:od:

%Y Cf. A180278.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jul 17 2011