A118224 - OEIS

%I #13 Sep 24 2024 16:26:39

%S 2,6,12,24,48,60,120,120,180,240,360,360,720,720,720,840,1260,1260,

%T 1680,1680,2520,2520,2520,2520,5040,5040,5040,5040,5040,5040,7560,

%U 7560,10080,10080,10080,10080,15120,15120,15120,15120,20160,20160,25200,25200,25200

%N Smallest number having at least 2*n divisors.

%H Michael S. Branicky, <a href="/A118224/b118224.txt">Table of n, a(n) for n = 1..1000</a>

%F A000005(a(n)) >= 2*n;

%F a(n) = A061799(2*n).

%F a(n) <= A003680(n). - _Michael S. Branicky_, Feb 06 2021

%t s={};Do[i=1;Until[DivisorSigma[0,i]>=2n,i++];AppendTo[s,i],{n,45}];s (* _James C. McMahon_, Sep 24 2024 *)

%o (Python)

%o from sympy import divisors

%o def a(n):

%o   m = 4*n - 2

%o   while len(divisors(m)) < 2*n: m += 1

%o   return m

%o print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Feb 06 2021

%Y Cf. A086921, A003680 (exactly 2n).

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 16 2006