

A038549


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


6



1, 4, 12, 24, 36, 60, 192, 120, 180, 240, 576, 360, 1296, 900, 720, 840, 9216, 1260, 786432, 1680, 2880, 15360, 3600, 2520, 6480, 61440, 6300, 6720, 2359296, 5040, 3221225472, 7560, 46080, 983040, 25920, 10080, 206158430208, 32400, 184320
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OFFSET

1,2


COMMENTS

Least number of identical objects that can be arranged in exactly n ways in a rectangle, modulo rotation.
Smallest number which has n distinct unordered factorizations of the form x*y.  Lekraj Beedassy, Jan 09 2008
Note that an upper bound on a(n) is 3*2^(n1), which is attained at n = 4 and the odd primes in A005382 (primes p such that 2p1 is also prime).  T. D. Noe, Jul 13 2013


LINKS

Paul Tek, Table of n, a(n) for n = 1..1000
T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.


FORMULA

a(n) = min(A005179(2n1), A005179(2n)).


MATHEMATICA

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 *)


PROG

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a038549 = (+ 1) . fromJust . (`elemIndex` a038548_list)
 Reinhard Zumkeller, Dec 26 2012


CROSSREFS

Cf. A038548 (records), A072671, A004778, A086921.
Cf. A227068 (similar, but with limit < sqrt).
Sequence in context: A008103 A086921 A004778 * A008081 A008188 A057322
Adjacent sequences: A038546 A038547 A038548 * A038550 A038551 A038552


KEYWORD

nonn


AUTHOR

Tom Verhoeff (Tom.Verhoeff(AT)acm.org)


EXTENSIONS

More terms from David W. Wilson.


STATUS

approved



