cp's OEIS Frontend

A262207 a(n) = prime(n)^n mod n^n.

%I A262207 #33 Jun 15 2025 13:17:27
%S A262207 0,1,17,97,1676,21241,214259,5020449,34808102,7233300201,46070142226,
%T A262207 7806783217105,165239209697109,1608006723911113,48560388990668468,
%U A262207 4867006141797699265,530779430908845468654,18442832496573633213385
%N A262207 a(n) = prime(n)^n mod n^n.
%C A262207 Inspired by A002380, A067602, A138654.
%C A262207 a(3), a(4), a(7) and a(48) are prime numbers.
%C A262207 There are no further prime numbers up to a(1000). - _Harvey P. Dale_, Jun 15 2025
%H A262207 Harvey P. Dale, <a href="/A262207/b262207.txt">Table of n, a(n) for n = 1..386</a>
%F A262207 a(n) = A062457(n) mod A000312(n). - _Michel Marcus_, Sep 15 2015
%e A262207 For n = 1, a(n) = prime(1)^1 mod 1^1 = 2^1 mod 1 = 2 mod 1 = 0.
%e A262207 For n = 2, a(n) = prime(2)^2 mod 2^2 = 3^2 mod 4 = 9 mod 4 = 1.
%e A262207 For n = 3, a(n) = prime(3)^3 mod 3^3 = 5^3 mod 27 = 125 mod 27 = 17.
%t A262207 Table[Mod[Prime[n]^n, n^n], {n, 18}] (* _Michael De Vlieger_, Sep 15 2015 *)
%t A262207 Table[PowerMod[Prime[n],n,n^n],{n,20}] (* _Harvey P. Dale_, Jun 15 2025 *)
%o A262207 (PARI) a(n) = (prime(n)^n) % (n^n);
%o A262207 vector(18, n, a(n))
%Y A262207 Cf. A002380, A067602, A138654, A000312, A062457, A121623.
%K A262207 nonn,easy
%O A262207 1,3
%A A262207 _Altug Alkan_, Sep 15 2015