A338151 - OEIS

%I #8 Oct 17 2020 10:53:17

%S 9,4,9,16,25,169,25,64,81,100,25,27,729,121,49,256,289,324,81,64,243,

%T 484,49,576,5929,676,169,784,121,125,225,100,1089,841,7921,1000,343,

%U 196,81,1600,169,216,441,361,2025,2116,289,2304,2401,256,625,2704,2809,441

%N a(n) = (n+1)^A338136(n) mod n^A338150(n).

%C a(n) is a perfect power, and a(n) == 1 + n*A338136(n) (mod n^2).

%H Jinyuan Wang, <a href="/A338151/b338151.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = (n+1)^A338136(n) mod n^A338150(n).

%e a(2) = 3^A338136(2) mod 2^A338150(2) = 3^6 mod 2^4 = 3^2 = 9.

%e a(13) = 14^A338136(13) mod 13^A338150(13) = 14^2 mod 13^2 = 3^3 = 27.

%p g:= proc(n) local k, x, j, F;

%p   for k from 2 to n-2 do

%p    x:= (n+1)^k;

%p    for j from 2 to floor(k*log[n](n+1)) do

%p      F:= ifactors(x mod (n^j))[2];

%p      if igcd(op(map(t -> t[2], F))) > 1 then return x mod (n^j) fi

%p   od od

%p end proc:

%p g(2):= 9: g(3):= 4:

%p map(g, [$2..40]);

%Y Cf. A338136, A338150.

%K nonn

%O 2,1

%A _J. M. Bergot_ and _Robert Israel_, Oct 12 2020