This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A097275 #5 Feb 16 2025 08:32:54 %S A097275 1,2,3,6,4,12,18,8,15,60,30,9,24,105,420,54,16,36,120,840,4620,90,27, %T A097275 45,180,1155,9240,60060,162,32,48,240,1260,13860,120120,1021020,210, %U A097275 64,72,315,1680,15015,180180,2042040,19399380,270,81,96,360,2520,18480,240240 %N A097275 Least integer "mod 2 prime signatures" k ordered by number of primitive Pythagorean triples with leg = k. %C A097275 Row 0 of table represents "mod 2 prime signature" values k such that no PPTs have leg=k. %C A097275 Row n of table, n>0, represents "mod 2 prime signature" values k such that 2^(n-1) PPTs have leg=k. Table read by antidiagonals. %C A097275 For n=2^a_0*p_1^a_1*...*p_n^a_n where p_i is odd prime and a_1>=a_2>=...>=a_n, define "mod 2 prime signature" to be ordered prime exponents (a_0,a_1,...,a_n). %C A097275 Least integer with a given "mod 2 prime signature" is obtained by replacing p_1 with 3, p_2 with 5,..., p_n with n-th odd prime. %H A097275 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a> %e A097275 Table begins: %e A097275 0: 1,2,6,18,30,54,90,162,210,270,... %e A097275 1: 3,4,8,9,16,27,32,64,81,128,... %e A097275 2: 12,15,24,36,45,48,72,96,108,135,... %e A097275 4: 60,105,120,180,240,315,360,480,540,720,... %e A097275 8: 420,840,1155,1260,1680,2520,3360,3465,3780,5040,... %e A097275 16: 4620,9240,13860,15015,18480,27720,36960,41580,45045,55440,... %e A097275 32: 60060,120120,180180,240240,255255,360360,480480,540540,... %e A097275 64: 1021020,2042040,3063060,4084080,4849845,6126120,8168160,... %e A097275 128: 19399380,38798760,58198140,77597520,111546435,116396280,... %e A097275 256: 446185740,892371480,1338557220,1784742960,2677114440,... %Y A097275 Cf. A097272, A097273, A097274. %Y A097275 Row 1 is A006899 except for starting point. %K A097275 nonn,tabl %O A097275 0,2 %A A097275 _Ray Chandler_, Aug 22 2004