A254734 a(n) is the least k > n such that n divides k^4.

2, 4, 6, 6, 10, 12, 14, 10, 12, 20, 22, 18, 26, 28, 30, 18, 34, 24, 38, 30, 42, 44, 46, 30, 30, 52, 30, 42, 58, 60, 62, 36, 66, 68, 70, 42, 74, 76, 78, 50, 82, 84, 86, 66, 60, 92, 94, 54, 56, 60, 102, 78, 106, 60, 110, 70, 114, 116, 118, 90, 122, 124, 84

Offset: 1

Author

Peter Kagey, Feb 07 2015

Keywords

• nonn

Comments

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

a(n) = 2*n iff n is squarefree (A005117). - Robert Israel, Feb 08 2015

Examples

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

Links

• Peter Kagey, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A005117 (squarefree).

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

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

Programs

Maple

f:= proc(n) local k;
     for k from n+1 do if (k^4/n)::integer then return k fi od:
end proc:
seq(f(n), n=1..100); # Robert Israel, Feb 08 2015

Mathematica

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

PARI

a(n)=for(k=n+1,2*n,if(k^4%n==0,return(k)))
vector(100,n,a(n)) \\ Derek Orr Feb 07 2015

Python

def A254734(n):
    k = n + 1
    while pow(k, 4, n):
        k += 1
    return k # Chai Wah Wu, Feb 15 2015

Ruby

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