A336442 Numbers having 3 pairwise coprime divisors, {d_1, d_2, d_3}, such that d_1 < d_2 < d_3 < 2*d_1.

60, 120, 140, 180, 210, 240, 280, 300, 315, 360, 420, 462, 480, 504, 540, 560, 600, 616, 630, 660, 693, 700, 720, 728, 770, 780, 792, 819, 840, 900, 910, 924, 936, 945, 960, 980, 990, 1001, 1008, 1020, 1050, 1080, 1092, 1120, 1140, 1144, 1170, 1200, 1232, 1260

Offset: 1

Author

Amiram Eldar, Jul 21 2020

Keywords

• nonn

Comments

Erdős (1970) proved that the asymptotic density of this sequence exists and is less than 1.

The numbers of terms not exceeding 10^k for k = 1, 2, ... are 0, 1, 37, 543, 6529, 73578, 798916, 8480417, 88832422, ...

Any positive multiple of any term of this sequence is also a term. The primitive terms are in A336443.

Examples

			60 is a term since {3, 4, 5} are divisors of 60, gcd(3,4) = gcd(4,5) = gcd(3,5) = 1 and 3 < 4 < 5 < 2*3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Erdős, Some extremal problems in combinatorial number theory, in the book Hari Shankar (ed.), Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio (1970), pp. 123-133.

Crossrefs

Subsequence of A005279.

A336443 is a subsequence.

Programs

Mathematica

divQ[n_] := AnyTrue[Subsets[Divisors[n], {3}], And @@ CoprimeQ @@@ Subsets[#, {2}] && #[[3]] < 2 * #[[1]] &]; Select[Range[1500], divQ]