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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 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified December 21 23:06 EST 2014. Contains 252326 sequences.