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A097274 Least integer "mod 2 prime signatures" k ordered by number of Pythagorean triples with leg = k.

%I A097274 #5 Feb 16 2025 08:32:54
%S A097274 1,2,3,4,6,8,9,18,16,27,54,12,15,30,32,81,162,64,243,486,128,729,1458,
%T A097274 24,36,45,90,256,2187,4374,512,6561,13122,1024,19683,39366,48,108,135,
%U A097274 270,2048,59049,118098,4096,177147,354294,72,225,450,8192,531441
%N A097274 Least integer "mod 2 prime signatures" k ordered by number of Pythagorean triples with leg = k.
%C A097274 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 A097274 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 A097274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>
%e A097274 Table begins:
%e A097274 0: 1,2,
%e A097274 1: 3,4,6,
%e A097274 2: 8,9,18,
%e A097274 3: 16,27,54,
%e A097274 4: 12,15,30,32,81,162,
%e A097274 5: 64,243,486,
%e A097274 6: 128,729,1458,
%e A097274 7: 24,36,45,90,256,2187,4374,
%e A097274 8: 512,6561,13122,
%e A097274 9: 1024,19683,39366,
%e A097274 10: 48,108,135,270,2048,59049,118098,
%e A097274 11: 4096,177147,354294,
%e A097274 12: 72,225,450,8192,531441,1062882,
%Y A097274 Cf. A097272, A097273, A097275.
%K A097274 nonn,tabf
%O A097274 0,2
%A A097274 _Ray Chandler_, Aug 22 2004