A248662 Numbers with the property: tau(n) > sopfr(n), or A000005(n) > A001414(n).

1, 120, 144, 180, 216, 240, 252, 288, 300, 336, 360, 420, 432, 480, 504, 540, 576, 600, 630, 648, 660, 672, 720, 756, 792, 810, 840, 864, 900, 960, 1008, 1050, 1080, 1120, 1152, 1176, 1200, 1260, 1296, 1320, 1344, 1350, 1400, 1440, 1500, 1512, 1560

Offset

1,2

Comments

The number of divisors exceeds the sum of its prime factors, with repetition.

These are a subset of the abundant numbers = A005101.

The numbers where tau(n) = sopfr(n) are given by A078511.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

ResultList = {1}; Do[
If[ (DivisorSigma[0, k] > Total[Times @@@ FactorInteger[k]]),
  AppendTo[ResultList, k]], {k, 2, 10000}]; ResultList

Prog

(PARI) isok(n) = my(f=factor(n)); sum(i=1, #f~, f[i, 1]*f[i, 2]) < numdiv(n); \\ Michel Marcus, Jun 22 2019

Crossrefs

Cf. A000005, A001414, A005101, A078511.

Sequence in context: A297152 A074302 A095631 * A259826 A192277 A034291

Adjacent sequences: A248659 A248660 A248661 * A248663 A248664 A248665

Keyword

nonn

Author

Richard R. Forberg, Jan 15 2015

Extensions

a(1) = 1 inserted by Amiram Eldar, Jun 22 2019

Status

approved