%I #10 Mar 02 2018 02:13:42
%S 1,3,8,15,24,36,48,72,96,140,180,280,336,420,480,672,864,900,1008,
%T 1080,1260,1980,2340,3744,4032,4680,6048,9450,11088,11880,13440,16632,
%U 17280,30888,32400,33264,33600,44352,46800,47520,63360,66528,71280,84240
%N Where A174102 sets a new record.
%H Robert G. Wilson v, <a href="/A173570/b173570.txt">Table of n, a(n) for n = 1..109</a>
%t f[n_] := Length@ Split[ Divisors@n, #2 - #1 == 1 &] (* f(n) from Dr. Bobby R. Treat *); t = Table[0, {1000}]; k = 1; While[k < 10^9, a = f@k; If[a < 101 && t[[a]] == 0, t[[a]] = k; Print[{k, a}]]; k++ ]; lst = {1}; m = 1; While[m < 1001, If[ t[[m]] > lst[[ -1]], AppendTo[ lst, t[[m]]]]; m++ ]; lst
%Y Cf. A137921, A173569.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Feb 22 2010