A097626 Numbers k that are the hypotenuse of exactly 67 distinct integer-sided right triangles, i.e., k^2 can be written as a sum of two squares in 67 ways.

160225, 204425, 226525, 292825, 320450, 337025, 348725, 386425, 403325, 408850, 416585, 453050, 456025, 480675, 491725, 493025, 499525, 505325, 531505, 535925, 544765, 558025, 574925, 585650, 588965, 602225, 613275, 624325, 637325, 640900

Offset

1,1

Comments

If m is a term, then 2*m and p*m are terms where p is any prime of the form 4j+3. - Chai Wah Wu, Feb 29 2016

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Chai Wah Wu)

Mathematica

r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[300000], Length[r[#]] == 67 &] (* Vincenzo Librandi, Mar 01 2016 *)

Crossrefs

Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40).

Sequence in context: A206674 A205518 A141816 * A212081 A251827 A115536

Adjacent sequences: A097623 A097624 A097625 * A097627 A097628 A097629

Keyword

nonn

Author

James R. Buddenhagen, Sep 20 2004

Extensions

More terms from Ray Chandler, Sep 21 2004

Status

approved