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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 (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 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
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
Sequence in context: A100599 A353440 A198390 * A254064 A257224 A092433
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 March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)