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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)