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%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