A097282 Numbers k that are the hypotenuse of exactly 40 distinct integer-sided right triangles, i.e., k^2 can be written as a sum of two squares in 40 ways.

32045, 40885, 45305, 58565, 64090, 67405, 69745, 77285, 80665, 81770, 90610, 91205, 96135, 98345, 98605, 99905, 101065, 107185, 111605, 114985, 117130, 120445, 122655, 124865, 127465, 128180, 128945, 130645, 134810, 135915, 137605

Offset: 1

Author

James R. Buddenhagen, Sep 17 2004

Keywords

• nonn

Comments

k^2 is always the sum of k^2 and 0^2, but no real triangle can have a zero-length side. Thus, the Mathematica program below searches for length 41 and implicitly drops the zero-squared-plus-n-squared solution. - Harvey P. Dale, Dec 09 2010

If m is a term, then 2*m and p*m are terms where p is any prime of the form 4j+3. - Ray Chandler, Dec 30 2019

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

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), A097626 (67).

Programs

Mathematica

Select[Range[150000],Length[PowersRepresentations[#^2,2,2]]==41&] (* Harvey P. Dale, Dec 09 2010 *)