A068317 Numbers n such that n*tau(n) > omega(n)*prime(n) where tau(n) is the number of divisors of n and omega(n) the number of distinct prime factors of n.

1, 2, 3, 4, 8, 9, 16, 24, 27, 32, 36, 48, 64, 72, 96, 108, 128, 144, 160, 180, 192, 216, 240, 256, 288, 320, 324, 360, 384, 400, 432, 480, 504, 512, 540, 576, 600, 640, 648, 672, 720, 756, 768, 792, 800, 840, 864, 896, 900, 936, 960, 972, 1000, 1008, 1024

Offset

1,2

Comments

There are very few odd terms in the sequence: 1, 3, 9, 27, 30375, 33075,...

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[1040], #*DivisorSigma[0, #] > PrimeNu[#]*Prime[#] &] (* Ivan Neretin, Mar 16 2017 *)

Prog

(PARI) for(n=1, 1000, if(numdiv(n)*n>omega(n)*prime(n), print1(n, ", ")))

Crossrefs

Sequence in context: A078829 A045583 A045608 * A074311 A076382 A006899

Adjacent sequences: A068314 A068315 A068316 * A068318 A068319 A068320

Keyword

easy,nonn

Author

Benoit Cloitre, Feb 26 2002

Status

approved