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 A137425 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. 1
 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 1080, 1440, 2160, 2880, 3600, 4320, 5040, 7560, 10080, 15120, 20160, 25200, 30240, 45360, 60480, 75600, 98280, 131040, 166320, 221760, 277200, 332640, 498960, 665280, 831600, 1081080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE 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. MAPLE 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 CROSSREFS Sequence in context: A166981 A004394 A189686 * A141320 A307122 A309015 Adjacent sequences:  A137422 A137423 A137424 * A137426 A137427 A137428 KEYWORD nonn AUTHOR J. Lowell, Apr 17 2008 EXTENSIONS More terms from R. J. Mathar, Mar 20 2010 STATUS approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)