A075592 Numbers n such that number of distinct prime divisors of n is a divisor of n.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 83, 84, 86, 88, 89, 90

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• easy
• nonn

Comments

Numbers n such that omega(n) divides n.

The asymptotic density of this sequence is 0 (Cooper and Kennedy, 1989). - Amiram Eldar, Jul 10 2020

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
• Curtis N. Cooper, Robert E. Kennedy, Chebyshev's inequality and natural density, Amer. Math. Monthly 96 (1989), no. 2, 118-124.

Crossrefs

Different from A070776: 78 belongs to this sequence but not to A070776.

Cf. A185307 (complement), A001221, A001222, A074946 (BigOmega(n) divides n).

Programs

Mathematica

Select[Range[2,100],Divisible[#,Length[Select[Divisors[#], PrimeQ]]]&]  (* Harvey P. Dale, Mar 17 2011 *)

PARI

isok(n) = iferr(!(n % omega(n)), E, 0); \\ Michel Marcus, Oct 06 2017

R

library(gmp); omega<-function(x) length(unique(as.numeric(factorize(x))))
which(c(F,vapply(2:100,function(n) isint(n/omega(n)),T))) # Christian N. K. Anderson, Apr 25 2013

Extensions

More terms from David Wasserman, Jan 20 2005

"Distinct" added to name by Christian N. K. Anderson, Apr 23 2013