

A185307


Numbers not divisible by the number of their distinct prime factors.


6



1, 15, 21, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 70, 75, 77, 85, 87, 91, 93, 95, 99, 110, 111, 115, 117, 119, 123, 129, 130, 133, 135, 140, 141, 143, 145, 147, 153, 154, 155, 159, 161, 170, 171, 175, 177, 182, 183, 185, 187, 189, 190, 201, 203, 205, 207, 209
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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. 118124.


EXAMPLE

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


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

Cf. A075592 (complement), A001221, A001222, A074946, A134334.
Sequence in context: A184041 A070005 A275384 * A061346 A098905 A225375
Adjacent sequences: A185304 A185305 A185306 * A185308 A185309 A185310


KEYWORD

nonn


AUTHOR

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


STATUS

approved



