A254734 - OEIS

%I #39 Sep 20 2024 17:12:18

%S 2,4,6,6,10,12,14,10,12,20,22,18,26,28,30,18,34,24,38,30,42,44,46,30,

%T 30,52,30,42,58,60,62,36,66,68,70,42,74,76,78,50,82,84,86,66,60,92,94,

%U 54,56,60,102,78,106,60,110,70,114,116,118,90,122,124,84

%N a(n) is the least k > n such that n divides k^4.

%C A073353(n) <= a(n) <= 2*n. Any prime that divides n must also divide a(n), and because n divides (2*n)^4.

%C a(n) = 2*n iff n is squarefree (A005117). - _Robert Israel_, Feb 08 2015

%H Peter Kagey, <a href="/A254734/b254734.txt">Table of n, a(n) for n = 1..5000</a>

%e a(16) = 18 because 16 divides 18^4, but 16 does not divide 17^4.

%p f:= proc(n) local k;

%p      for k from n+1 do if (k^4/n)::integer then return k fi od:

%p end proc:

%p seq(f(n), n=1..100); # _Robert Israel_, Feb 08 2015

%t lk[n_]:=Module[{k=n+1},While[PowerMod[k,4,n]!=0,k++];k]; Array[lk,70] (* _Harvey P. Dale_, Nov 22 2015 *)

%o (Ruby)

%o def a(n)

%o   (n+1..2*n).find { |k| k**4 % n == 0 }

%o end

%o (PARI) a(n)=for(k=n+1,2*n,if(k^4%n==0,return(k)))

%o vector(100,n,a(n)) \\ _Derek Orr_ Feb 07 2015

%o (Python)

%o def A254734(n):

%o     k = n + 1

%o     while pow(k, 4, n):

%o         k += 1

%o     return k # _Chai Wah Wu_, Feb 15 2015

%Y Cf. A005117 (squarefree).

%Y Cf. A073353 (similar, with k^n).

%Y Cf. A254732 (similar, with k^2), A254733 (similar, with k^3).

%K nonn

%O 1,1

%A _Peter Kagey_, Feb 07 2015