A328708 Number of non-primitive Pythagorean triples with leg n.

0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 5, 1, 1, 2, 2, 0, 4, 0, 3, 2, 1, 2, 5, 0, 1, 2, 5, 0, 4, 0, 2, 5, 1, 0, 8, 1, 2, 2, 2, 0, 3, 2, 5, 2, 1, 0, 9, 0, 1, 5, 4, 2, 4, 0, 2, 2, 4, 0, 10, 0, 1, 5, 2, 2, 4, 0, 8, 3, 1, 0, 9, 2, 1, 2, 5, 0, 7, 2, 2, 2, 1, 2, 11, 0, 2, 5, 5, 0, 4

Offset: 1

Author

Rui Lin, Oct 26 2019

Keywords

• nonn

Comments

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

This sequence is the count of n as leg in non-primitive Pythagorean triple.

Examples

			n=3 as leg in only one primitive Pythagorean triple, (3,4,5); so a(3)=0.
n=6 as leg in only one non-primitive Pythagorean triple, (6,8,10); so a(6)=1.
n=8 as leg in one primitive Pythagorean triple (8,15,17) and in one non-primitive Pythagorean triple (6,8,10); so a(8)=1.
		

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

Crossrefs

Cf. A046079, A024361.

Formula

a(n) = A046079(n) - A024361(n).