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a(n) is the unique positive integer m such that n < m*sqrt(A261865(n)) < n + 1.
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%I #15 May 07 2021 17:51:47

%S 1,2,2,3,4,4,5,6,7,6,8,9,8,10,11,12,10,13,14,12,15,16,9,17,18,19,16,

%T 20,21,8,22,23,24,20,25,26,14,27,28,18,29,30,31,20,32,33,18,34,35,36,

%U 30,37,38,15,39,40,41,34,42,43,25,44,45,37,46,47,48,28,49

%N a(n) is the unique positive integer m such that n < m*sqrt(A261865(n)) < n + 1.

%H Peter Kagey, <a href="/A343205/b343205.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 23, a(23) = 9 because A261865(n) = 7 and 23 < 9*sqrt(7) < 24.

%t A343205[n_] := (k = 2;

%t While[Ceiling[Sqrt[(n + 1)^2/k]] - Floor[Sqrt[n^2/k]] < 2, k++];

%t Ceiling[n/Sqrt[k]]) (* Based on Michael De Vlieger's A261865 program *)

%Y Cf. A261865.

%K nonn

%O 1,2

%A _Peter Kagey_, Apr 08 2021