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A275616 Numbers n such that n and omega(n) are relatively prime, where omega(n) (A001221) is the number of distinct prime divisors of n. 2
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 70, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 110, 111, 113, 115, 117, 119, 121, 123, 125, 127, 128, 129, 130, 131, 133, 135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alladi shows that the density of A063743 is 6/Pi^2, and mentions (p. 229) that a slight modification of the proof shows that the density of this sequence is the same, hence a(n) ~ (Pi^2/6)n.

Vol'kovič (1976) proved that the asymptotic density of this sequence is 6/Pi^2. - Amiram Eldar, Jul 10 2020

REFERENCES

József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter V, p. 174.

V. E. Vol'kovič, Numbers that are relatively prime to their number of prime divisors (in Russian), Izv. Akad. Nauk USSR Ser. Fiz.-Math. Nauk, Vol. 86, No. 4 (1976), pp. 3-7.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Krishnaswami Alladi, On the probability that n and Omega(n) are relatively prime, Fibonacci Quarterly 19:3 (1981), pp. 228-232.

PROG

(PARI) is(n)=gcd(omega(n), n)==1

CROSSREFS

Cf. A063743, A001221.

Sequence in context: A213715 A078174 A174894 * A088948 A115405 A343857

Adjacent sequences:  A275613 A275614 A275615 * A275617 A275618 A275619

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Aug 03 2016

STATUS

approved

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Last modified September 21 05:02 EDT 2021. Contains 347596 sequences. (Running on oeis4.)