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A097754 Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of primitive Pythagorean triples with hypotenuse = k.

%I A097754 #10 Feb 16 2025 08:32:54
%S A097754 1,2,5,3,25,65,4,125,325,1105,6,625,1625,5525,32045,8,3125,4225,27625,
%T A097754 160225,1185665,9,15625,8125,71825,801125,5928325,48612265,10,78125,
%U A097754 21125,138125,2082925,29641625,243061325,2576450045,12,390625,40625
%N A097754 Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of primitive Pythagorean triples with hypotenuse = k.
%C A097754 See A097751 for definition of "mod 4 prime signature".
%C A097754 Row 0 of table represents "mod 4 prime signature" values k such that no PPTs have hypotenuse=k.
%C A097754 Row n of table, n>0, represents "mod 4 prime signature" values k such that 2^(n-1) PPTs have hypotenuse=k.
%H A097754 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>
%e A097754 Table begins:
%e A097754 0: 1,2,3,4,6,8,9,10,12,15,16,18,20,21,24,27,30,...
%e A097754 1: 5,25,125,625,3125,15625,78125,390625,1953125,...
%e A097754 2: 65,325,1625,4225,8125,21125,40625,105625,203125,...
%e A097754 4: 1105,5525,27625,71825,138125,359125,690625,1221025,...
%e A097754 8: 32045,160225,801125,2082925,4005625,10414625,20028125,...
%e A097754 16: 1185665,5928325,29641625,77068225,148208125,385341125,...
%e A097754 32: 48612265,243061325,1215306625,3159797225,6076533125,...
%e A097754 64: 2576450045,12882250225,64411251125,167469252925,...
%e A097754 128: 157163452745,785817263725,3929086318625,10215624428425,...
%e A097754 256: 11472932050385,57364660251925,286823301259625,...
%Y A097754 Cf. A097751, A097752, A097753, A097755, A097756.
%Y A097754 Row 1 is A000351 except for starting point.
%K A097754 nonn,tabl
%O A097754 1,2
%A A097754 _Ray Chandler_, Aug 26 2004
%E A097754 Correct offset. _Ray Chandler_, Jan 15 2013