A256098 - OEIS

%I #16 Feb 15 2025 12:16:03

%S 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,

%T 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,

%U 1,1,16,8,16,4,16,8,16,2,16,8,16,4,16,8,16,1

%N Denominators for the numerators A256097.

%C The corresponding numerators are given in A256097.

%C See A256097 for comments, references and links.

%H Stefano Spezia, <a href="/A256098/b256098.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%e See A256097.

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

%Y Cf. A000196, A048760, A048761, A256097.

%K nonn,easy,frac,changed

%O 1,2

%A _Wolfdieter Lang_, Mar 24 2015

%E a(61)-a(80) from _Stefano Spezia_, Feb 15 2025