cp's OEIS Frontend

A327898 a(n) is the nearest integer to the reciprocal of the difference between the square root of n and the nearest integer to this square root unless n is a perfect square, in which case a(n) equals 0.

%I A327898 #41 Oct 03 2019 16:44:36
%S A327898 0,2,-4,0,4,2,-3,-6,0,6,3,2,-3,-4,-8,0,8,4,3,2,-2,-3,-5,-10,0,10,5,3,
%T A327898 3,2,-2,-3,-4,-6,-12,0,12,6,4,3,2,2,-2,-3,-3,-5,-7,-14,0,14,7,5,4,3,2,
%U A327898 2,-2,-3,-3,-4,-5,-8,-16,0,16,8,5,4,3,3,2,2,-2,-3
%N A327898 a(n) is the nearest integer to the reciprocal of the difference between the square root of n and the nearest integer to this square root unless n is a perfect square, in which case a(n) equals 0.
%C A327898 If n is a perfect square, i.e., 1, 4, 9, or 16, then the computation is not possible and a(n) is given as 0.
%H A327898 Michel Marcus, <a href="/A327898/b327898.txt">Table of n, a(n) for n = 1..10000</a>
%F A327898 a(n) = round(1/(sqrt(n)-round(sqrt(n)))) for n not a square; a(n) = 0 otherwise.
%t A327898 Array[If[IntegerQ@ #2, 0, Round[1/(#2 - Round[#2])]] & @@ {#, Sqrt@ #} &, 64] (* _Michael De Vlieger_, Sep 29 2019 *)
%o A327898 (PARI) a(n)={if(issquare(n), 0, my(t=sqrt(n)); round(1/(t-round(t))))} \\ _Andrew Howroyd_, Sep 30 2019
%Y A327898 Cf. A000290 (squares), A013942, A091453 (if floor is used instead of round).
%K A327898 sign
%O A327898 1,2
%A A327898 _Sebastian F. Orellana_, Sep 29 2019