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%I #17 Feb 10 2024 04:00:35
%S 1,2,6,12,30,36,84,120,180,240,660,720,1560,1260,1680,2880,6120,5040,
%T 15960,10080,15120,27720,115920,83160,138600,196560,302400,277200,
%U 803880,498960,1562400,665280,720720,1413720,1441440,2162160,8205120
%N a(1)=1. a(n) is the smallest positive multiple of n that has more divisors than a(n-1) has.
%H Amiram Eldar, <a href="/A143176/b143176.txt">Table of n, a(n) for n = 1..89</a> (terms 1..60 from Michael De Vlieger)
%e a(4)=12 has 6 divisors. Checking the multiples of 5: 1*5=5 has 2 divisors. 2*5=10 has 4 divisors. 3*5=15 has 4 divisors. 4*5=20 has 6 divisors. 5*5=25 has 3 divisors. So the first 5 positive multiples of 5 each have <= 6 divisors. But 6*5 = 30 has 8 divisors. And since 8 > 6, a(5) = 30.
%t FoldList[Block[{d = DivisorSigma[0, #1], k = 1, m}, While[DivisorSigma[0, Set[m, k #2]] <= d, k++]; m] &, Range@ 37] (* _Michael De Vlieger_, Aug 29 2017 *)
%Y Cf. A143177, A143178.
%K nonn
%O 1,2
%A _Leroy Quet_, Jul 28 2008
%E a(9)-a(37) from _Donovan Johnson_, Sep 05 2008
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