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A328949 Number of non-primitive Pythagorean triples with n as a leg or the hypotenuse. 2
0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 3, 2, 0, 2, 0, 3, 2, 1, 0, 5, 2, 2, 2, 2, 0, 5, 0, 3, 2, 2, 3, 5, 0, 1, 3, 6, 0, 4, 0, 2, 6, 1, 0, 8, 1, 4, 3, 3, 0, 3, 3, 5, 2, 2, 0, 10, 0, 1, 5, 4, 4, 4, 0, 3, 2, 5, 0, 10, 0, 2, 7, 2, 2, 5, 0, 9, 3, 2, 0, 9, 4, 1, 3, 5, 0, 8, 3, 2, 2, 1, 3, 11, 0, 2, 5, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Pythagorean triples including primitive ones and non-primitive ones. For a certain n, it may be a leg or the hypotenuse in either a primitive Pythagorean triple, or a non-primitive Pythagorean triple, or both.

This sequence is the count of n as a leg or the hypotenuse in non-primitive Pythagorean triples.

REFERENCES

A. Beiler, Recreations in the Theory of Numbers. New York: Dover Publications, pp. 116-117, 1966.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 5000 terms from Metin Sariyar)

FORMULA

a(n) = A328708(n) + A328712(n).

a(n) = A046081(n) - A024363(n).

EXAMPLE

For n=10, 10 is a leg in (10,24,26) and the hypotenuse in (6,8,10), so a(10)=A328708(10)+A328712(10)=1+1=2. And 10 is not a leg or the hypotenuse in any primitive Pythagorean triple, a(10)=A046081(10)-A024363(10)=2-0=2.

MATHEMATICA

a[n_] := Count[{x, y} /. Solve[(x^2 + y^2 == n^2 || x^2 - y^2 == n^2) && x > y > 0, {x, y}, Integers], p_ /; GCD @@ p > 1]; Array[a, 100] (* Giovanni Resta, Nov 01 2019 *)

CROSSREFS

Cf. A328708, A328712, A046081, A024363.

Sequence in context: A064984 A323226 A307197 * A038555 A138108 A158777

Adjacent sequences:  A328946 A328947 A328948 * A328950 A328951 A328952

KEYWORD

nonn

AUTHOR

Rui Lin, Nov 01 2019

STATUS

approved

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Last modified September 26 23:32 EDT 2020. Contains 337378 sequences. (Running on oeis4.)