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%I #6 Oct 03 2015 22:56:38
%S 1,2,4,6,12,24,36,48,60,120,180,240,360,720,1080,1440,2160,2880,3600,
%T 4320,5040,7560,10080,15120,20160,25200,30240,45360,60480,75600,98280,
%U 131040,166320,221760,277200,332640,498960,665280,831600,1081080
%N a(1) = 1;l for n>1, a(n) = smallest number such that: 1. the number of divisors is strictly increasing, 2. the differences between the terms are nondecreasing.
%e 840 with 32 divisors cannot be the term after 720 because 720 - 360 = 360 and 840 - 720 is 120 < 360. On the other hand, 1080 (also with 32 divisors) can because 720 - 360 = 360 and 1080 - 720 = 360 >= 360.
%p A137425 := proc(n) option remember; local a,tprev ; if n <= 3 then 2^(n-1); else tprev := numtheory[tau](procname(n-1)) ; for a from 2*procname(n-1)-procname(n-2) do if numtheory[tau](a) > tprev then return a; end if; end do: end if; end proc: seq(A137425(n),n=1..43) ; # _R. J. Mathar_, Mar 20 2010
%K nonn
%O 1,2
%A _J. Lowell_, Apr 17 2008
%E More terms from _R. J. Mathar_, Mar 20 2010
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