A328499 The number of primitive Pythagorean triangles with perimeter less than n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

1,30

Comments

D. N. Lehmer has proved that the asymptotic density of a(n) is a(n)/n = log(2)/Pi^2 = 0.07023049... See A118858.

Links

Table of n, a(n) for n=1..100.

Ron Knott, Pythagorean Triples and Online Calculators

D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22, 293-335, 1900.

Example

For n=90, the triples are
   {3,  4,  5},  3 +  4 +  5 = 12 < 90
   {5, 12, 13},  5 + 12 + 13 = 30 < 90
   {7, 24, 25},  7 + 24 + 25 = 56 < 90
   {8, 15, 17},  8 + 15 + 17 = 40 < 90
   {9, 40, 41},  9 + 40 + 41 = 90
  {12, 35, 37}, 12 + 35 + 37 = 84 < 90
  {20, 21, 29}, 20 + 21 + 29 = 70 < 90
so a(90)=7.

Crossrefs

Cf. A008846, A024364, A118858, A249750.

Sequence in context: A111897 A185711 A185712 * A339183 A135665 A135662

Adjacent sequences: A328496 A328497 A328498 * A328500 A328501 A328502

Keyword

nonn,easy

Author

Mo Li, Oct 17 2019

Status

approved