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A165159 Long legs in primitive Pythagorean triangles with three side lengths of composite integers. 3
56, 63, 77, 117, 120, 143, 153, 156, 171, 176, 187, 220, 224, 240, 247, 253, 273, 304, 323, 345, 352, 357, 360, 364, 377, 396, 403, 416, 435, 437, 456, 460, 468, 475, 476, 483, 493, 513, 525, 527, 528, 544, 561, 621, 624, 627, 644, 663, 665, 667, 672, 680 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence collects the numbers B such that A^2+B^2=C^2, A<B<C, gcd(A,B,C)=1 and such that all

three of A, B and C are in A002808. If there are two or more triangles of this kind with the same B,

like (A,B,C) = (1003,1596,1885) and (A,B,C) = (1403,1596,2125), only one instance

of B is added to the sequence.

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

(A,B,C)=(33,56,65) contributes B=56 to the sequence. (A,B,C)=(16,63,65) contributes B=63 to the sequence.

MATHEMATICA

lst={}; Do[Do[If[IntegerQ[c=Sqrt[a^2+b^2]] && GCD[a, b, c]==1, If[ !PrimeQ[a]&&!PrimeQ[b] && !PrimeQ[c], AppendTo[lst, b]]], {a, b-1, 3, -1}], {b, 4, 2000, 1}]; Union@lst

CROSSREFS

Cf. A020882, A020883, A165158, A165160.

Sequence in context: A069810 A292896 A154768 * A336265 A039428 A043251

Adjacent sequences:  A165156 A165157 A165158 * A165160 A165161 A165162

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 06 2009

EXTENSIONS

Edited by R. J. Mathar, Oct 02 2009

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)