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.

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

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.

Mathematica

Select[Range[200], CoprimeQ[#, PrimeNu[#]]&] (* Harvey P. Dale, Dec 20 2021 *)

Prog

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

Crossrefs

Cf. A063743, A001221.

Sequence in context: A360552 A078174 A174894 * A088948 A369096 A115405

Adjacent sequences: A275613 A275614 A275615 * A275617 A275618 A275619

Keyword

nonn

Author

Charles R Greathouse IV, Aug 03 2016

Status

approved