A097753 - OEIS

%I #13 Feb 16 2025 08:32:54

%S 1,2,5,3,10,25,4,15,50,125,6,20,75,250,65,8,30,100,375,130,3125,9,40,

%T 150,500,195,6250,15625,12,45,200,750,260,9375,31250,325,16,60,225,

%U 1000,390,12500,46875,650,390625,18,80,300,1125,520,18750,62500,975

%N Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of Pythagorean triples with hypotenuse = k.

%C See A097751 for definition of "mod 4 prime signature".

%C Row 0 of table represents "mod 4 prime signature" values k such that no PTs have hypotenuse=k.

%C Row n of table, n>0, represents "mod 4 prime signature" values k such that n PTs have hypotenuse=k.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

%e Table begins:

%e 0: 1,2,3,4,6,8,9,12,16,18,21,...

%e 1: 5,10,15,20,30,40,45,60,80,90,105,...

%e 2: 25,50,75,100,150,200,225,300,400,450,525,...

%e 3: 125,250,375,500,750,1000,1125,1500,2000,2250,2625,...

%e 4: 65,130,195,260,390,520,585,625,780,1040,1170,...

%e 5: 3125,6250,9375,12500,18750,25000,28125,37500,...

%e 6: 15625,31250,46875,62500,93750,125000,140625,...

%e 7: 325,650,975,1300,1950,2600,2925,3900,5200,...

%e 8: 390625,781250,1171875,1562500,2343750,...

%e 9: 1953125,3906250,5859375,7812500,11718750,...

%e 10: 1625,3250,4875,6500,9750,13000,14625,19500,...

%Y Cf. A097751, A097752, A097754, A097755, A097756.

%K nonn,tabl,changed

%O 1,2

%A _Ray Chandler_, Aug 26 2004

%E Correct offset. _Ray Chandler_, Jan 15 2013