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

1, 2, 3, 4, 6, 8, 9, 18, 16, 27, 54, 12, 15, 30, 32, 81, 162, 64, 243, 486, 128, 729, 1458, 24, 36, 45, 90, 256, 2187, 4374, 512, 6561, 13122, 1024, 19683, 39366, 48, 108, 135, 270, 2048, 59049, 118098, 4096, 177147, 354294, 72, 225, 450, 8192, 531441

Offset

0,2

Comments

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).

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.

Links

Table of n, a(n) for n=0..50.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Example

Table begins:
0: 1,2,
1: 3,4,6,
2: 8,9,18,
3: 16,27,54,
4: 12,15,30,32,81,162,
5: 64,243,486,
6: 128,729,1458,
7: 24,36,45,90,256,2187,4374,
8: 512,6561,13122,
9: 1024,19683,39366,
10: 48,108,135,270,2048,59049,118098,
11: 4096,177147,354294,
12: 72,225,450,8192,531441,1062882,

Crossrefs

Cf. A097272, A097273, A097275.

Sequence in context: A160256 A151545 A353383 * A322572 A375564 A254438

Adjacent sequences: A097271 A097272 A097273 * A097275 A097276 A097277

Keyword

nonn,tabf,changed

Author

Ray Chandler, Aug 22 2004

Status

approved