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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A317294 A095736 A004829 * A285801 A324109 A070776

Adjacent sequences: A075589 A075590 A075591 * A075593 A075594 A075595

Keyword

easy,nonn

Author

Amarnath Murthy, Sep 26 2002

Extensions

More terms from David Wasserman, Jan 20 2005

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

Status

approved