A118905 Sum of legs of Pythagorean triangles (without multiple entries).

7, 14, 17, 21, 23, 28, 31, 34, 35, 41, 42, 46, 47, 49, 51, 56, 62, 63, 68, 69, 70, 71, 73, 77, 79, 82, 84, 85, 89, 91, 92, 93, 94, 97, 98, 102, 103, 105, 112, 113, 115, 119, 123, 124, 126, 127, 133, 136, 137, 138, 140, 141, 142, 146, 147, 151, 153, 154, 155, 158, 161, 164, 167, 168, 170, 175, 178, 182, 184, 186, 187, 188

Offset: 1

Author

Giovanni Resta, May 05 2006

Keywords

• nonn

Comments

The prime numbers in this sequence define A001132 (see comment in A001132). - Richard Choulet, Dec 16 2008

For the sum of legs of Pythagorean triangles with multiple entries see A198390. - Wolfdieter Lang, May 24 2013

Are these just the positive multiples of A001132? - Charles R Greathouse IV, May 28 2013

For the sum of legs of primitive Pythagorean triangles see A120681. - Wolfdieter Lang, Feb 17 2015

n is in the sequence iff A331671(n) > 0. - Ray Chandler, Feb 26 2020

Examples

			7 = 3 + 4 and 3^2 + 4^2 = 5^2.
a(14) = 49 = 7^2 from the primitive Pythagorean triangle (x,y,z) = (9,40,41), and from the non-primitive one 7*(3,4,5); a(42) = 119 = 7*17 from four Pythagorean triangles (39,80,89) and (99,20,181) (both primitive) and 7*(5,12,13), 17*(3,4,5). - _Wolfdieter Lang_, May 24 2013
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Pythagorean Triple.

Crossrefs

Cf. A009096, A118903, A118904, A058529, A001132, A120681, A331671.

Programs

Magma

[m:m in [2..200]|#[k:k in [1..m-1]|IsSquare(k^2+(m-k)^2)] ne 0]; // Marius A. Burtea, Jul 29 2019

PARI

is(n)=my(t=n^2); forstep(i=2-n%2, n-2, 2, if(issquare((t+i^2)/2), return(1))); 0 \\ Charles R Greathouse IV, May 28 2013

Extensions

More terms from 147 on. - Richard Choulet, Nov 24 2009

Name specified. - Wolfdieter Lang, May 24 2013