A262207 - OEIS

%I #26 Jun 01 2016 06:42:11

%S 0,1,17,97,1676,21241,214259,5020449,34808102,7233300201,46070142226,

%T 7806783217105,165239209697109,1608006723911113,48560388990668468,

%U 4867006141797699265,530779430908845468654,18442832496573633213385

%N a(n) = prime(n)^n mod n^n.

%C Inspired by A002380, A067602, A138654.

%C a(3), a(4), a(7) and a(48) are prime numbers.

%F a(n) = A062457(n) mod A000312(n). - _Michel Marcus_, Sep 15 2015

%e For n = 1, a(n) = prime(1)^1 mod 1^1 = 2^1 mod 1 = 2 mod 1 = 0.

%e For n = 2, a(n) = prime(2)^2 mod 2^2 = 3^2 mod 4 = 9 mod 4 = 1.

%e For n = 3, a(n) = prime(3)^3 mod 3^3 = 5^3 mod 27 = 125 mod 27 = 17.

%t Table[Mod[Prime[n]^n, n^n], {n, 18}] (* _Michael De Vlieger_, Sep 15 2015 *)

%o (PARI) a(n) = (prime(n)^n) % (n^n);

%o vector(18, n, a(n))

%Y Cf. A002380, A067602, A138654, A000312, A062457, A121623.

%K nonn,easy

%O 1,3

%A _Altug Alkan_, Sep 15 2015