A066955 Number of unordered solutions of x*y + y*z + z*x = n, x,y,z > 0.

0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 3, 2, 1, 2, 3, 1, 3, 0, 3, 3, 2, 1, 4, 2, 1, 2, 4, 2, 4, 0, 2, 4, 3, 1, 5, 3, 2, 2, 4, 2, 3, 2, 4, 5, 2, 0, 6, 2, 3, 3, 5, 3, 4, 2, 2, 5, 4, 0, 7, 3, 2, 4, 5, 4, 4, 0, 5, 6, 4, 1, 6, 4, 2, 4, 6, 2, 6, 2, 4, 5, 2, 3, 8, 6, 2, 3, 6, 2, 7, 0, 5, 8, 4

Offset: 1

Author

Colin Mallows, Jan 26 2002

Keywords

• nonn
• easy

Comments

a(n) is the number of distinct rectangular cuboids each one having integer surface area 2*n and integer edge lengths x, y and z. - Felix Huber, Aug 08 2023

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000196, A066360, A094379.

Programs

Haskell

a066955 n = length [(x,y,z) | x <- [1 .. a000196 (div n 3)],
                              y <- [x .. div n x],
                              z <- [y .. div (n - x*y) (x + y)],
                              x * y + (x + y) * z == n]
-- Reinhard Zumkeller, Mar 23 2012

PARI

a(n)=sum(i=1,n,sum(j=1,i,sum(k=1,j,if(i*j+j*k+k*i-n,0,1))))

Formula

a(A094379(n)) = n and a(m) = n for m < A094379(n). - Reinhard Zumkeller, Mar 23 2012

Extensions

More terms from Benoit Cloitre, Feb 02 2003