A097274 - OEIS

%I #5 Feb 16 2025 08:32:54

%S 1,2,3,4,6,8,9,18,16,27,54,12,15,30,32,81,162,64,243,486,128,729,1458,

%T 24,36,45,90,256,2187,4374,512,6561,13122,1024,19683,39366,48,108,135,

%U 270,2048,59049,118098,4096,177147,354294,72,225,450,8192,531441

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

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

%e Table begins:

%e 0: 1,2,

%e 1: 3,4,6,

%e 2: 8,9,18,

%e 3: 16,27,54,

%e 4: 12,15,30,32,81,162,

%e 5: 64,243,486,

%e 6: 128,729,1458,

%e 7: 24,36,45,90,256,2187,4374,

%e 8: 512,6561,13122,

%e 9: 1024,19683,39366,

%e 10: 48,108,135,270,2048,59049,118098,

%e 11: 4096,177147,354294,

%e 12: 72,225,450,8192,531441,1062882,

%Y Cf. A097272, A097273, A097275.

%K nonn,tabf,changed

%O 0,2

%A _Ray Chandler_, Aug 22 2004