

A328949


Number of nonprimitive 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
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OFFSET

1,10


COMMENTS

Pythagorean triples including primitive ones and nonprimitive ones. For a certain n, it may be a leg or the hypotenuse in either a primitive Pythagorean triple, or a nonprimitive Pythagorean triple, or both.
This sequence is the count of n as a leg or the hypotenuse in nonprimitive Pythagorean triples.


REFERENCES

A. Beiler, Recreations in the Theory of Numbers. New York: Dover Publications, pp. 116117, 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)=20=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



