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A061799 Smallest number with at least n divisors. 13
1, 2, 4, 6, 12, 12, 24, 24, 36, 48, 60, 60, 120, 120, 120, 120, 180, 180, 240, 240, 360, 360, 360, 360, 720, 720, 720, 720, 720, 720, 840, 840, 1260, 1260, 1260, 1260, 1680, 1680, 1680, 1680, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 5040, 5040, 5040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Smallest number which can be expressed as the least common multiple of n distinct numbers. - Amarnath Murthy, Nov 27 2002

Also smallest possible member of a set of n+1 numbers with pairwise distinct GCD's. [Following an observation by Charles R Greathouse IV] (Proof: If the smallest number min(S) of the set (with card(S)=n+1) has a distinct GCD with each of the other n numbers, then it must have at least n distinct divisors (because any GCD is a divisor). It is then easy to choose larger members of the set so that all pairs of elements have pairwise distinct GCD's, e.g., by successively multiplying by distinct and sufficiently large primes.) - M. F. Hasler, Mar 05 2013

LINKS

T. D. Noe, Table of n, a(n) for n=1..2000 (using A002182)

EXAMPLE

a(5)=12 since every number less than 12 has fewer than five divisors (1 has one; 2,3,5,7 and 11 have two each; 4 and 9 have three each; 6,8 and 10 have four each) while 12 has at least five (in fact it has six: 1,2,3,4,6 and 12).

MATHEMATICA

Reap[ For[ n = 1, n <= 100, n++, s = n; While[ DivisorSigma[0, s] < n, s++]; Sow[s] ] ][[2, 1]] (* Jean-Fran├žois Alcover, Feb 16 2012, after Pari *)

PROG

(PARI) for(n=1, 100, s=n; while(numdiv(s)<n, s++); print1(s, ", "))

(Haskell)

import Data.List (findIndex)

import Data.Maybe (fromJust)

a061799 n = succ $ fromJust $ findIndex (n <=) $ map a000005 [1..]

-- Reinhard Zumkeller, Apr 01 2011

CROSSREFS

Cf. A000005, A002182, A002183, A005179, A213918.

Sequence in context: A053146 A056675 A062857 * A076868 A056793 A137387

Adjacent sequences:  A061796 A061797 A061798 * A061800 A061801 A061802

KEYWORD

nice,nonn

AUTHOR

Henry Bottomley, Jun 22 2001

EXTENSIONS

Replaced "factors" by "divisors" in definition and example M. F. Hasler, Oct 24 2010

STATUS

approved

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Last modified October 2 02:22 EDT 2014. Contains 247527 sequences.