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

1,1

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

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

Example

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.

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 &]

Prog

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

Crossrefs

Cf. A024355, A024361, A042965.

Sequence in context: A117815 A154390 A346608 * A050696 A144266 A162826

Adjacent sequences: A156680 A156681 A156682 * A156684 A156685 A156686

Keyword

easy,nice,nonn

Author

Ant King, Feb 17 2009

Status

approved