A141037 Numbers n where the sum of all of its divisors <= sqrt(n) exceeds the sum of all the divisors of m <= sqrt(m) for all m<n.

1, 4, 9, 12, 16, 24, 30, 36, 60, 72, 90, 120, 144, 180, 240, 336, 360, 420, 480, 504, 600, 630, 672, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3600, 3780, 3960, 4200, 4320, 4620, 5040, 6720, 7560, 9240, 10080, 12600, 13860, 15120, 18480, 20160

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..250

Example

12 qualifies because it sets a record of 1+2+3=6. (1, 2 and 3 are the divisors of 12 <= sqrt(12).)

Mathematica

lst = {}; s = -1; Do[t = Plus @@ Select[Divisors@n, # <= Sqrt@n &]; If[t > s, AppendTo[lst, n]; s = t], {n, 25199}]; lst (* Robert G. Wilson v, Aug 03 2008 *)

Crossrefs

Cf. A002093 (all divisors), A034090 (all divisors except n itself).

Cf. A066839, A143837 (records of sums).

Sequence in context: A292226 A225870 A171920 * A109424 A034019 A034018

Adjacent sequences: A141034 A141035 A141036 * A141038 A141039 A141040

Keyword

nonn

Author

J. Lowell, Jul 28 2008

Extensions

More terms from Robert G. Wilson v, Aug 03 2008

Status

approved