OFFSET

1,2

COMMENTS

The complement of A075592 (omega(n) divides n).

Though initially sparse, the sequence increases in density. There are more numbers divisible by omega(n) than not from [3,9265], but there are always more indivisible numbers thereafter.

There are 308 more numbers divisible than indivisible in the range from 1 to 2754, 2778, and 2880. This three values are the global maxima.

The asymptotic density of this sequence is 1 (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 and Robert E. Kennedy, Chebyshev's inequality and natural density, Amer. Math. Monthly, Vol. 96, No. 2 (1989), pp. 118-124.

EXAMPLE

The distinct prime factors of 45 are 3 and 5, but 45 is not divisible by 2.

MATHEMATICA

Join[{1}, Select[Range[2, 300], Mod[#, PrimeNu[#]]!=0&]] (* Harvey P. Dale, Jun 05 2023 *)

PROG

(R) library(numbers); isint<-function(x) x==as.integer(x); which(!vapply(1:500, function(n) isint(n/omega(n)), T))

(PARI) isok(n) = iferr(n % omega(n), E, 1); \\ Michel Marcus, Jul 10 2020

CROSSREFS

KEYWORD

nonn

AUTHOR

Christian N. K. Anderson and Kevin L. Schwartz, Apr 23 2013

STATUS

approved