

A165160


Short legs in primitive Pythagorean triangles with three side lengths of composite integers.


2



16, 21, 24, 27, 33, 36, 44, 55, 56, 57, 60, 63, 64, 68, 75, 76, 77, 81, 84, 87, 88, 91, 92, 93, 96, 99, 100, 104, 105, 111, 115, 116, 117, 119, 120, 123, 124, 125, 128, 129, 132, 133, 135, 136, 140, 143, 144, 147, 152, 153, 155, 156, 160, 161, 164, 165, 168, 172
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OFFSET

1,1


COMMENTS

The sequence collects the numbers A 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 A,
like (A,B,C) = (33,544,545) and (A,B,C) = (33,56,65), only one instance
of A is added to the sequence.


LINKS

Table of n, a(n) for n=1..58.


EXAMPLE

(A,B,C) = (16,63,65) contributes A=16 to the sequence. (A,B,C)= (21,220,221) contributes A=21.
Further length triples are (24,143,145), (27,364,365), (33,56,65), (33,544,545), (36,77,85),
(36,323,325), (44,117,125), (44,483,485), (55,1512,1513), (56,783,785), (57,176,185)G.


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, a]]], {b, a+1, Floor[a^2/2], 1}], {a, 3, 400, 1}]; Union@lst


CROSSREFS

Cf. A009004, A020882, A020883, A165158, A165159
Sequence in context: A186462 A205098 A290142 * A180411 A050436 A038868
Adjacent sequences: A165157 A165158 A165159 * A165161 A165162 A165163


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 06 2009


EXTENSIONS

Edited by R. J. Mathar, Oct 02 2009


STATUS

approved



