# solutions to n +a(1) +a(2) +..+a(j) = a(1)a(2)..a(j)

Leroy Quet qq-quet at mindspring.com
Tue Sep 23 03:59:44 CEST 2003

Let n and j be any fixed positive integers.

How many sequences of j positive integers
{a(1), a(2), ...,a(j)}

satisfy the equation:

n +a(1) +a(2) +a(3) +..+a(j) = 
a(1) *a(2) *a(3) *...*a(j)


Fixing j and finding a closed-form of the number of solutions in-terms of 
n might be interesting.

For example, for j = 2, the number of solutions is

d(n+1), the number of positive divisors of (n+1).

(I think.)

There must be a recursive-definition, anyhow, to find the number of 
solutions with j a's (in terms of n) from the numbers of solutions for 
(j-1) a's, as a possibility.

Leroy Quet

More information about the SeqFan mailing list