

A118905


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


8



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
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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 primitive Pythagorean triangles see A120681.  Wolfdieter Lang, Feb 17 2015
n is in the sequence iff A331671(n) > 0.  Ray Chandler, Feb 26 2020


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 nonprimitive 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=2n%2, n2, 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..m1]IsSquare(k^2+(mk)^2)] ne 0]; // Marius A. Burtea, Jul 29 2019


CROSSREFS

Cf. A009096, A118903, A118904, A058529, A001132, A120681, A331671.
Sequence in context: A336797 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



