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%I #7 Aug 06 2019 14:25:17
%S 1,2,3,4,5,6,8,9,11,13,15,18,21,24,27,31,35,39,44,49,55,61,68,75,83,
%T 92,101,112,122,134,147,161,175,191,208,227,246,267,289,313,339,366,
%U 396,427,460,495,533,573,616,661,709,760,815,872,934,998,1067,1140
%N Least positive integer k such that 1 + 1/2 + ... + 1/k >= sqrt(n).
%H Clark Kimberling, <a href="/A226189/b226189.txt">Table of n, a(n) for n = 1..150</a>
%e a(12) = 18 because 1 + 1/2 + ... + 1/17 < sqrt(12) < 1 + 1/2 + ... + 1/18.
%t z = 80; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= Sqrt[n] &], {n, 1, z}]; m = Map[a, Range[z]]
%t Table[Ceiling[x /. FindInstance[HarmonicNumber[x] == Sqrt[n] && x > 0, x][[1]]], {n, 80}] (* _Vladimir Reshetnikov_, Aug 06 2019 *)
%Y Cf. A226183, A226190.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 30 2013
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