cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

Colin Mallows, Jan 26 2002

Keywords

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

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

A067754 Number of unordered primitive solutions to xy+xz+yz=n.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 4, 2, 3, 2, 3, 3, 4, 2, 4, 4, 2, 4, 3, 2, 4, 4, 4, 3, 4, 3, 6, 3, 2, 4, 6, 4, 5, 4, 3, 4, 4, 3, 6, 4, 3, 4, 6, 3, 4, 4, 6, 6, 4, 2, 7, 4, 4, 5, 6, 3, 6, 6, 3, 5, 6, 4, 8, 4, 3, 6, 6, 4, 6, 4, 6, 6, 4, 3, 7, 6, 4, 6, 8, 4, 7, 6, 6, 4, 4, 5, 10, 6, 3, 5, 6, 3
Offset: 1

Views

Author

Colin Mallows, Jan 31 2002

Keywords

Comments

For n = m^2 this is the number of root Descartes quadruples (-m,b,c,d).
An upper bound on the number of solutions appears to be 1.5*sqrt(n). - T. D. Noe, Jun 14 2006

Examples

			a(9)=2 because of (0,1,9) and (1,1,4) (but not (0,3,3)).

Links

Crossrefs

Cf. A067751, A067752, A067753.

Programs

  • Mathematica
    Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z] && GCD[x,y,z]==1, cnt++ ], {x,0,Sqrt[n/3]}, {y, Max[1,x],Sqrt[x^2+n]-x}]; cnt, {n,100}] (* T. D. Noe, Jun 14 2006 *)

Formula

a(n) = A066360(n) + A007875(n). - T. D. Noe, Jun 14 2006

Extensions

Corrected and extended by T. D. Noe, Jun 14 2006
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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