A319813 - OEIS

%I #8 Oct 03 2018 10:37:38

%S 1,1,2,0,4,0,6,0,2,3,10,0,12,0,14,0,16,0,18,0,5,0,22,0,4,5,2,0,28,0,

%T 30,0,32,13,34,0,36,0,17,0,40,0,42,0,14,0,46,0,6,3,50,0,52,0,19,0,8,

%U 17,58,0,60,0,5,0,64,0,66,0,68,0,70,0,72,31,14,0,76

%N a(n) is the smallest a such that n is divisible by a^n + 1, or 0 if no such a exists.

%C a(n) = 0 iff n is even and -1 is not a square modulo n, that is, n is even and not in A008784. For other n > 2, 2 <= a(n) <= n - 1.

%C a(p) = p - 1 for primes p. For composite n, a(n) = n - 1 iff gcd(n, phi(n)) = 1, that is, n is in A050384.

%C a(A006521(n)) = 2.

%H Jianing Song, <a href="/A319813/b319813.txt">Table of n, a(n) for n = 1..7000</a>

%F For n = 9, 9 is divisible by a^9 + 1 implies a == 2 (mod 3), so a(9) = 2.

%F For n = 10, 10 is divisible by a^10 + 1 implies a == 3, 7 (mod 10), so a(10) = 3.

%F For n = 34, 34 is divisible by a^34 + 1 implies a == 13, 21 (mod 34), so a(34) = 13.

%o (PARI) a(n) = if(!(n%2)&&!issquare(Mod(-1,n)), 0, my(i=1); while(Mod(i,n)^n!=n-1, i++); i)

%Y Cf. A074792 (a^n - 1 instead of a^n + 1).

%Y Cf. also A006521, A008784, A050384.

%K nonn

%O 1,3

%A _Jianing Song_, Sep 28 2018