A256098 Denominators for the numerators A256097.

1, 2, 1, 1, 4, 2, 4, 1, 1, 6, 3, 2, 3, 6, 1, 1, 8, 4, 8, 2, 8, 4, 8, 1, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 1, 1, 14, 7, 14, 7, 14, 7, 2, 7, 14, 7, 14, 7, 14, 1, 1, 16, 8, 16, 4, 16, 8, 16, 2, 16, 8, 16, 4, 16, 8, 16, 1

Offset: 1

Author

Wolfdieter Lang, Mar 24 2015

Keywords

• nonn
• easy
• frac

Comments

The corresponding numerators are given in A256097.

See A256097 for comments, references and links.

Examples

			See A256097.
		

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000196, A048760, A048761, A256097.

Programs

Mathematica

A000196[n_]:=Floor[Sqrt[n]]; a[n_]:=Denominator[(A000196[n]+n/A000196[n])/2]; Array[a,80](* Stefano Spezia, Feb 15 2025 *)

Formula

a(n) = denominator(R(n)), with the rational (in lowest terms) R(n) = f(n) + (n - f(n)^2)/(2*f(n)) = (f(n) + n/f(n))/2 with f(n) := floor(sqrt(n)) = A000196(n), for n >= 1.

Extensions

a(61)-a(80) from Stefano Spezia, Feb 15 2025