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

1,1

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.

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.

Example

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.

Mathematica

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

Crossrefs

Subsequence of A005279.

A336443 is a subsequence.

Sequence in context: A252961 A252962 A296767 * A096490 A056866 A098136

Adjacent sequences: A336439 A336440 A336441 * A336443 A336444 A336445

Keyword

nonn

Author

Amiram Eldar, Jul 21 2020

Status

approved