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A038549 Least number with exactly n divisors that are at most its square root.

%I A038549 #29 Mar 22 2017 13:53:47
%S A038549 1,4,12,24,36,60,192,120,180,240,576,360,1296,900,720,840,9216,1260,
%T A038549 786432,1680,2880,15360,3600,2520,6480,61440,6300,6720,2359296,5040,
%U A038549 3221225472,7560,46080,983040,25920,10080,206158430208,32400,184320
%N A038549 Least number with exactly n divisors that are at most its square root.
%C A038549 Least number of identical objects that can be arranged in exactly n ways in a rectangle, modulo rotation.
%C A038549 Smallest number which has n distinct unordered factorizations of the form x*y. - _Lekraj Beedassy_, Jan 09 2008
%C A038549 Note that an upper bound on a(n) is 3*2^(n-1), which is attained at n = 4 and the odd primes in A005382 (primes p such that 2p-1 is also prime). - _T. D. Noe_, Jul 13 2013
%H A038549 Paul Tek, <a href="/A038549/b038549.txt">Table of n, a(n) for n = 1..1000</a>
%H A038549 T. Verhoeff, <a href="https://cs.uwaterloo.ca/journals/JIS/trapzoid.html">Rectangular and Trapezoidal Arrangements</a>, J. Integer Sequences, Vol. 2, 1999, #99.1.6.
%F A038549 a(n) = min(A005179(2n-1), A005179(2n)).
%t A038549 nn = 18; t = Table[0, {nn}]; found = 0; n = 0; While[found < nn, n++; c = Length[Select[Divisors[n], # <= Sqrt[n] &]]; If[c > 0 && c <= nn && t[[c]] == 0, t[[c]] = n; found++]]; t (* _T. D. Noe_, Jul 10 2013 *)
%o A038549 (Haskell)
%o A038549 import Data.List (elemIndex)
%o A038549 import Data.Maybe (fromJust)
%o A038549 a038549 = (+ 1) . fromJust . (`elemIndex` a038548_list)
%o A038549 -- _Reinhard Zumkeller_, Dec 26 2012
%Y A038549 Cf. A038548 (records), A072671, A004778, A086921.
%Y A038549 Cf. A227068 (similar, but with limit < sqrt).
%K A038549 nonn
%O A038549 1,2
%A A038549 _Tom Verhoeff_
%E A038549 More terms from _David W. Wilson_.