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A185307
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Numbers not divisible by the number of their distinct prime factors.
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6
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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
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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The distinct prime factors of 45 are 3 and 5, but 45 is not divisible by 2.
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MATHEMATICA
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Join[{1}, Select[Range[2, 300], Mod[#, PrimeNu[#]]!=0&]] (* Harvey P. Dale, Jun 05 2023 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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