A097275 Least integer "mod 2 prime signatures" k ordered by number of primitive Pythagorean triples with leg = k.

1, 2, 3, 6, 4, 12, 18, 8, 15, 60, 30, 9, 24, 105, 420, 54, 16, 36, 120, 840, 4620, 90, 27, 45, 180, 1155, 9240, 60060, 162, 32, 48, 240, 1260, 13860, 120120, 1021020, 210, 64, 72, 315, 1680, 15015, 180180, 2042040, 19399380, 270, 81, 96, 360, 2520, 18480, 240240

Offset

0,2

Comments

Row 0 of table represents "mod 2 prime signature" values k such that no PPTs have leg=k.

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.

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..51.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Example

Table begins:
0: 1,2,6,18,30,54,90,162,210,270,...
1: 3,4,8,9,16,27,32,64,81,128,...
2: 12,15,24,36,45,48,72,96,108,135,...
4: 60,105,120,180,240,315,360,480,540,720,...
8: 420,840,1155,1260,1680,2520,3360,3465,3780,5040,...
16: 4620,9240,13860,15015,18480,27720,36960,41580,45045,55440,...
32: 60060,120120,180180,240240,255255,360360,480480,540540,...
64: 1021020,2042040,3063060,4084080,4849845,6126120,8168160,...
128: 19399380,38798760,58198140,77597520,111546435,116396280,...
256: 446185740,892371480,1338557220,1784742960,2677114440,...

Crossrefs

Cf. A097272, A097273, A097274.

Row 1 is A006899 except for starting point.

Sequence in context: A273317 A328443 A122866 * A130879 A119741 A268216

Adjacent sequences: A097272 A097273 A097274 * A097276 A097277 A097278

Keyword

nonn,tabl

Author

Ray Chandler, Aug 22 2004

Status

approved