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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-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)

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Last modified August 12 02:13 EDT 2020. Contains 336435 sequences. (Running on oeis4.)