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
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from T. D. Noe)
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-François Alcover, Feb 16 2012, after Pari *)
With[{ds=Table[{n, DivisorSigma[0, n]}, {n, 6000}]}, Table[SelectFirst[ds, #[[2]] >= k&], {k, 60}]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 15 2019 *)
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
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