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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A005117 (squarefree).

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

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

Sequence in context: A037225 A060685 A073353 * A254733 A254732 A299541

Adjacent sequences: A254731 A254732 A254733 * A254735 A254736 A254737

Keyword

nonn

Author

Peter Kagey, Feb 07 2015

Status

approved