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A118905 Sum of legs of Pythagorean triangles (without multiple entries). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 prinitive Pythagorean triangles see A120681. - Wolfdieter Lang, Feb 17 2015

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Pythagorean Triple.

EXAMPLE

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

PROG

(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

(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

CROSSREFS

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

Sequence in context: A167197 A100599 A198390 * A254064 A257224 A092433

Adjacent sequences:  A118902 A118903 A118904 * A118906 A118907 A118908

KEYWORD

nonn

AUTHOR

Giovanni Resta, May 05 2006

EXTENSIONS

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

Name specified. - Wolfdieter Lang, May 24 2013

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)