cp's OEIS Frontend

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.

%I A097282 #20 Sep 05 2021 18:25:08
%S A097282 32045,40885,45305,58565,64090,67405,69745,77285,80665,81770,90610,
%T A097282 91205,96135,98345,98605,99905,101065,107185,111605,114985,117130,
%U A097282 120445,122655,124865,127465,128180,128945,130645,134810,135915,137605
%N 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.
%C A097282 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
%C A097282 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
%H A097282 Ray Chandler, <a href="/A097282/b097282.txt">Table of n, a(n) for n = 1..10000</a>
%t A097282 Select[Range[150000],Length[PowersRepresentations[#^2,2,2]]==41&] (* _Harvey P. Dale_, Dec 09 2010 *)
%Y A097282 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).
%K A097282 nonn
%O A097282 1,1
%A A097282 _James R. Buddenhagen_, Sep 17 2004