A329205 Lexicographically last solution to Erdős's Last Equation in n variables, x_1*...*x_n = n*(x_1 + ... + x_n), with 1 <= x_1 <= ... <= x_n, written as triangle T(n,k), 1<=k<=n.

1, 4, 4, 3, 3, 3, 2, 2, 2, 6, 1, 1, 3, 5, 5, 1, 1, 2, 3, 3, 5, 1, 1, 1, 2, 3, 3, 7, 1, 1, 2, 2, 2, 2, 2, 4, 1, 1, 1, 1, 2, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 2, 2, 3, 10, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 11, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6

Offset

1,2

Comments

a(1) = T(1,1) = 1 assumed. Any number is a solution for n=1.

References

R. K. Guy, Sum equals product. in: Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, chapter D24, (2004), 299-301.

Links

Table of n, a(n) for n=1..78.

David A. Corneth, list of solutions and product of variables of solutions for n = 2..160, omitting ones.

Example

The triangle begins:
  1;
  4, 4;
  3, 3, 3;
  2, 2, 2, 6;
  1, 1, 3, 5, 5;
  1, 1, 2, 3, 3, 5;
  1, 1, 1, 2, 3, 3, 7;
  1, 1, 2, 2, 2, 2, 2, 4;

Crossrefs

Cf. A328910, A328980, A329206.

Sequence in context: A364128 A120886 A228777 * A023402 A073261 A209252

Adjacent sequences: A329202 A329203 A329204 * A329206 A329207 A329208

Keyword

nonn,tabl

Author

Hugo Pfoertner, Nov 08 2019

Status

approved