A063743 Numbers n such that n and Omega(n) are relatively prime, where Omega(n) is the number of prime divisors of n (with repetition).

1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 20, 21, 23, 25, 28, 29, 31, 32, 33, 35, 37, 39, 41, 43, 44, 47, 48, 49, 50, 51, 52, 53, 55, 57, 59, 61, 65, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 81, 83, 85, 87, 89, 91, 92, 93, 95, 97, 98, 101, 103, 107, 108, 109, 110, 111, 112

Offset

1,2

Comments

Numbers n such that Omega(n)^phi(n) == 1 (mod n), where Omega(n) is the number of prime divisors of n counted with multiplicity (A001222) and phi(n) is the Euler totient function (A000010). - Michel Lagneau, Dec 21 2012

Alladi shows that the density of this sequence is 6/Pi^2, that is, a(n) ~ (Pi^2/6)n. - Charles R Greathouse IV, Aug 03 2016

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

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

Mathematica

fQ[n_] := GCD[PrimeOmega[n], n] == 1; Select[Range@115, fQ] (* Robert G. Wilson v, Dec 24 2012 *)

Prog

(PARI) j=[]; for(n=1, 300, if(gcd(n, bigomega(n))==1, j=concat(j, n))); j
(PARI) n=0; for (m=1, 10^9, if (gcd(m, bigomega(m))==1, write("b063743.txt", n++, " ", m); if (n==1000, break))) \\ Harry J. Smith, Aug 29 2009

Crossrefs

Cf. A001222, A275616.

Sequence in context: A078643 A137698 A358978 * A353968 A144100 A359059

Adjacent sequences: A063740 A063741 A063742 * A063744 A063745 A063746

Keyword

nonn

Author

Jason Earls, Aug 13 2001

Status

approved