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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.

%I A275616 #18 Jan 05 2025 19:51:40
%S A275616 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,
%T A275616 41,43,45,47,49,51,53,55,57,59,61,63,64,65,67,69,70,71,73,75,77,79,81,
%U A275616 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
%N 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.
%C A275616 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.
%C A275616 Vol'kovič (1976) proved that the asymptotic density of this sequence is 6/Pi^2. - _Amiram Eldar_, Jul 10 2020
%D A275616 József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter V, p. 174.
%D A275616 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.
%H A275616 Charles R Greathouse IV, <a href="/A275616/b275616.txt">Table of n, a(n) for n = 1..10000</a>
%H A275616 Krishnaswami Alladi, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/19-3/alladi.pdf">On the probability that n and Omega(n) are relatively prime</a>, Fibonacci Quarterly 19:3 (1981), pp. 228-232.
%t A275616 Select[Range[200],CoprimeQ[#,PrimeNu[#]]&] (* _Harvey P. Dale_, Dec 20 2021 *)
%o A275616 (PARI) is(n)=gcd(omega(n),n)==1
%Y A275616 Cf. A063743, A001221.
%K A275616 nonn
%O A275616 1,2
%A A275616 _Charles R Greathouse IV_, Aug 03 2016