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

1,12

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.

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

Formula

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

Example

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.

Crossrefs

Cf. A046079, A024361.

Sequence in context: A147767 A113678 A305436 * A299480 A110249 A160756

Adjacent sequences: A328705 A328706 A328707 * A328709 A328710 A328711

Keyword

nonn

Author

Rui Lin, Oct 26 2019

Status

approved