A165160 Short legs in primitive Pythagorean triangles with three side lengths of composite integers.

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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 06 2009

Keywords

• nonn

Comments

The sequence collects the numbers A such that A^2+B^2 = C^2, AA002808. 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.

Examples

			(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).
		

Crossrefs

Cf. A002808, A009004, A020882, A020883, A165158, A165159.

Programs

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

Extensions

Edited by R. J. Mathar, Oct 02 2009