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%I #15 Nov 09 2023 20:18:11
%S 12,15,20,21,24,28,33,35,36,39,40,44,45,48,51,52,55,56,57,60,63,65,68,
%T 69,72,75,76,77,80,84,85,87,88,91,92,93,95,96,99,100,104,105,108,111,
%U 112,115,116,117,119,120,123,124,129,132,133,135,136,140,141,143,144
%N Integers that can occur as either leg in more than one primitive Pythagorean triple.
%C This is also the sequence of non-singly-even numbers that contain more than one distinct prime factor.
%C Integers n such that A024361(n)>1; subsequence of both A024355 and A042965. - _Ray Chandler_, Feb 03 2020
%D Beiler, Albert H.: Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134.
%H Charles R Greathouse IV, <a href="/A156683/b156683.txt">Table of n, a(n) for n = 1..10000</a>
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Right-angled Triangles and Pythagoras' Theorem</a>
%e As 15 is the second integer that can occur as either leg in more than one primitive Pythagorean triangle - (8,15,17) and (15,112,113) - then a(2)=15.
%t PrimitiveRightTriangleLegs[1]:=0;PrimitiveRightTriangleLegs[n_Integer?Positive]:=Module[{f=Transpose[FactorInteger[n]][[1]]},If[Mod[n,4]==2,0,2^(Length[f]-1)]];Select[Range[150],PrimitiveRightTriangleLegs[ # ]>1 &]
%o (PARI) is(n)=n%4!=2 && !isprimepower(n) && n>1 \\ _Charles R Greathouse IV_, Jun 17 2013
%Y Cf. A024355, A024361, A042965.
%K easy,nice,nonn
%O 1,1
%A _Ant King_, Feb 17 2009
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