A156683 Integers that can occur as either leg in more than one primitive Pythagorean triple.

12, 15, 20, 21, 24, 28, 33, 35, 36, 39, 40, 44, 45, 48, 51, 52, 55, 56, 57, 60, 63, 65, 68, 69, 72, 75, 76, 77, 80, 84, 85, 87, 88, 91, 92, 93, 95, 96, 99, 100, 104, 105, 108, 111, 112, 115, 116, 117, 119, 120, 123, 124, 129, 132, 133, 135, 136, 140, 141, 143, 144

Offset: 1

Author

Ant King, Feb 17 2009

Keywords

• easy
• nice
• nonn

Comments

This is also the sequence of non-singly-even numbers that contain more than one distinct prime factor.

Integers n such that A024361(n)>1; subsequence of both A024355 and A042965. - Ray Chandler, Feb 03 2020

Examples

			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.
		

References

• Beiler, Albert H.: Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Ron Knott, Right-angled Triangles and Pythagoras' Theorem

Crossrefs

Cf. A024355, A024361, A042965.

Programs

Mathematica

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 &]

PARI

is(n)=n%4!=2 && !isprimepower(n) && n>1 \\ Charles R Greathouse IV, Jun 17 2013