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

1,2

Comments

The corresponding numerators are given in A256097.

See A256097 for comments, references and links.

Links

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

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.

Example

See A256097.

Mathematica

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

Crossrefs

Cf. A000196, A048760, A048761, A256097.

Sequence in context: A054090 A239456 A122517 * A177276 A123199 A212282

Adjacent sequences: A256095 A256096 A256097 * A256099 A256100 A256101

Keyword

nonn,easy,frac,changed

Author

Wolfdieter Lang, Mar 24 2015

Extensions

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

Status

approved