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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..40.

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: A004394 A189686 A355304 * 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