A254733 a(n) is the least k > n such that n divides k^3.

2, 4, 6, 6, 10, 12, 14, 10, 12, 20, 22, 18, 26, 28, 30, 20, 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, 60, 56, 60, 102, 78, 106, 60, 110, 70, 114, 116, 118, 90, 122, 124, 84

Offset: 1

Author

Peter Kagey, Feb 06 2015

Keywords

• nonn
• easy

Comments

A073353(n) <= a(n) <= 2*n. Any prime that divides n must also divide a(n), and because n divides (2*n)^3.

Examples

			a(8) = 10 because 8 divides 10^3, but 8 does not divide 9^3.
		

Links

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

Crossrefs

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

Cf. A254732 (similar, with k^2), A254734 (similar, with k^4).

Cf. A019555 (similar without the restriction that a(n) > n).

Programs

Mathematica

lkn[n_]:=Module[{k=n+1},While[PowerMod[k,3,n]!=0,k++];k]; Array[lkn,70] (* Harvey P. Dale, Nov 23 2024 *)

PARI

a(n)=for(k=n+1,2*n,if(k^3%n==0,return(k)))
vector(100,n,a(n)) \\ Derek Orr, Feb 07 2015

Ruby

def a(n)
  (n+1..2*n).find { |k| k**3 % n == 0 }
end

Formula

a(n) = n + A019555(n).