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a(1)=1. a(n) is the smallest positive multiple of n that has more, or the same number of, divisors than a(n-1) has.
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%I #7 Sep 22 2014 17:27:18

%S 1,2,3,4,10,6,14,8,18,20,44,12,52,28,30,48,204,72,228,60,84,132,276,

%T 72,150,156,108,84,348,60,372,96,132,204,140,72,444,228,156,120,984,

%U 168,1032,264,180,828,1692,240,1176,600,1020,780,3180,540,660,504,1140,1740

%N a(1)=1. a(n) is the smallest positive multiple of n that has more, or the same number of, divisors than a(n-1) has.

%H Harvey P. Dale, <a href="/A143178/b143178.txt">Table of n, a(n) for n = 1..500</a>

%e a(10) = 20, which has 6 divisors. Checking, for n = 11: 1*11=11 has 2 divisors. 2*11=22 has 4 divisors. 3*11=33 has 4 divisors. Each of these positive multiples of 11 has < 6 divisors. But 4*11=44 has 6 divisors. And since 6 >=6, then a(11) = 44.

%t nxt[{n_,a_}]:=Module[{k=1},While[DivisorSigma[0,a]>DivisorSigma[ 0,k(n+1)], k++];{n+1,k(n+1)}]; Transpose[NestList[nxt,{1,1},60]][[2]] (* _Harvey P. Dale_, Sep 22 2014 *)

%Y Cf. A143176, A143179.

%K nonn

%O 1,2

%A _Leroy Quet_, Jul 28 2008

%E a(13)-a(58) from _Donovan Johnson_, Sep 05 2008