

A239618


Number of primitive Euler bricks with side length a < b < c < 10^n, i.e., in a boxed parameter space with dimension 10^n.


1




OFFSET

1,3


COMMENTS

An Euler brick is a cuboid of integer side dimensions a, b, c such that the face diagonals are integers. It is called primitive if gcd(a,b,c)=1.
Because the sides of a cuboid are permutable without changing its shape, the total number of primitive Euler bricks in the parameter space a, b, c < 10^n is b(n) = 6*a(n) = 0, 0, 30, 114, 390, ...


LINKS

Table of n, a(n) for n=1..8.
Eric Weisstein's World of Mathematics, Euler Brick
Index entries for sequences related to bricks


EXAMPLE

a(3) = 5, since there are the five primitive Euler bricks [44, 117, 240], [85, 132, 720], [140, 480, 693], [160, 231, 792], [240, 252, 275] with longest side length < 1000.


CROSSREFS

Cf. A031173, A031174, A031175, A239620.
Sequence in context: A025568 A001047 A099448 * A124806 A059509 A137745
Adjacent sequences: A239615 A239616 A239617 * A239619 A239620 A239621


KEYWORD

nonn,more


AUTHOR

Martin Renner, Mar 22 2014


EXTENSIONS

a(6)a(8) from Giovanni Resta, Mar 22 2014


STATUS

approved



