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%I #9 Aug 30 2017 11:12:55
%S 2,3,4,6,7,8,9,10,12,14,15,18,19,20,21,24,25,28,29,30,32,33,34,36,38,
%T 39,40,42,43,48,49,50,51,52,54,60,61,62,63,66,67,70,71,72,75,76,77,80,
%U 81,84,85,88,89,90,91,96,98,99,100,108,109,110,112,114,115,120,121,124,125
%N a(1)=2. a(n) = the smallest integer > a(n-1) such that d(a(n)) >= d(n), where d(n) = the number of divisors of n.
%C Starting the sequence with a(1)=1 instead would have lead to a(n) = n for all n, obviously.
%H Harvey P. Dale, <a href="/A161577/b161577.txt">Table of n, a(n) for n = 1..1000</a>
%t nxt[{n_,a_}]:=Module[{k=a+1,d=DivisorSigma[0,n+1]},While[DivisorSigma[0,k]<d,k++];{n+1,k}]; NestList[nxt,{1,2},80][[All,2]] (* _Harvey P. Dale_, Aug 30 2017 *)
%Y A137518, A161576, A161578
%K nonn
%O 1,1
%A _Leroy Quet_, Jun 14 2009
%E Extended beyond 20 by _R. J. Mathar_, Oct 24 2009