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A336442 Numbers having 3 pairwise coprime divisors, {d_1, d_2, d_3}, such that d_1 < d_2 < d_3 < 2*d_1. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 21 2020
STATUS
approved

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Last modified July 12 18:45 EDT 2024. Contains 374251 sequences. (Running on oeis4.)