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

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

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^(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

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(2n-1), 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 A301053 A008188

Adjacent sequences: A038546 A038547 A038548 * A038550 A038551 A038552

Keyword

nonn

Author

Tom Verhoeff

Extensions

More terms from David W. Wilson.

Status

approved