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A118224 Smallest number having at least 2*n divisors.

%I A118224 #13 Sep 24 2024 16:26:39
%S A118224 2,6,12,24,48,60,120,120,180,240,360,360,720,720,720,840,1260,1260,
%T A118224 1680,1680,2520,2520,2520,2520,5040,5040,5040,5040,5040,5040,7560,
%U A118224 7560,10080,10080,10080,10080,15120,15120,15120,15120,20160,20160,25200,25200,25200
%N A118224 Smallest number having at least 2*n divisors.
%H A118224 Michael S. Branicky, <a href="/A118224/b118224.txt">Table of n, a(n) for n = 1..1000</a>
%F A118224 A000005(a(n)) >= 2*n;
%F A118224 a(n) = A061799(2*n).
%F A118224 a(n) <= A003680(n). - _Michael S. Branicky_, Feb 06 2021
%t A118224 s={};Do[i=1;Until[DivisorSigma[0,i]>=2n,i++];AppendTo[s,i],{n,45}];s (* _James C. McMahon_, Sep 24 2024 *)
%o A118224 (Python)
%o A118224 from sympy import divisors
%o A118224 def a(n):
%o A118224   m = 4*n - 2
%o A118224   while len(divisors(m)) < 2*n: m += 1
%o A118224   return m
%o A118224 print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Feb 06 2021
%Y A118224 Cf. A086921, A003680 (exactly 2n).
%K A118224 nonn
%O A118224 1,1
%A A118224 _Reinhard Zumkeller_, Apr 16 2006