The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328505 Numbers k such that there exist three rationals in arithmetic progression whose product is k. 1
 1, 3, 6, 8, 10, 11, 13, 14, 15, 17, 21, 24, 25, 27, 28, 29, 31, 34, 35, 36, 39, 42, 43, 45, 46, 47, 48, 49, 52, 53, 55, 57, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 76, 78, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 93, 99, 101, 103, 104, 105, 106, 107, 109, 111, 112, 114, 118, 119, 120, 122, 123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that there exist rationals x, d such that k = x*(x^2-d^2). Numbers k such that the elliptic curve s^3 + t^2 - k^2 has rational points other than (s,t) = (0, +/- k). Namely, if (s,t) is a rational point on the curve with s <> 0, then we can take x=k/s, d=t/s. If k is in the sequence, then so is j^3*k for any j. LINKS Robert Israel, Table of n, a(n) for n = 1..1231 Math StackExchange, Prime numbers as the product of an arithmetic sequence EXAMPLE a(5) = 10 is in the sequence because (1, 5/2, 4) are three rationals in arithmetic progression whose product is 10. a(6) = 11 is in the sequence because (-9/2,-11/12,8/3) are three rationals in arithmetic progression whose product is 11. PROG (Sage) R = range(1, 100); S = []; for r in R: E = EllipticCurve([0, 0, 0, 0, r^2]); if (E.torsion_subgroup().order() > 3) or (E.rank(only_use_mwrank=False) > 0): S.append(r); S CROSSREFS Sequence in context: A329500 A287362 A055073 * A012132 A108769 A286754 Adjacent sequences: A328502 A328503 A328504 * A328506 A328507 A328508 KEYWORD nonn AUTHOR Robert Israel, Oct 22 2019 EXTENSIONS More terms from Robert Israel, Mar 02 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 07:21 EDT 2023. Contains 363045 sequences. (Running on oeis4.)