

A156683


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


2



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
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OFFSET

1,1


COMMENTS

This is also the sequence of nonsinglyeven 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. 104134.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Ron Knott, Rightangled 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: A163657 A117815 A154390 * A050696 A144266 A162826
Adjacent sequences: A156680 A156681 A156682 * A156684 A156685 A156686


KEYWORD

easy,nice,nonn


AUTHOR

Ant King, Feb 17 2009


STATUS

approved



