Consider a matrix nXn representing a multiplication table i.e. a_ij=i*j .
Determine the number of appearances of n in this matrix.

(In reply to re: possible approach a hint by Ady TZIDON)

A number will appear once in any row whose index is a factor of the number. 
If i is a factor of n, then n will appear in row i.

So the number of appearances is equivalent to the number of factors of n. 

Here's a good explaination for the number of factors a number has: http://perplexus.info/show.php?pid=7138&cid=45236

In response to Ady's suggestion of 84,100,450

84,100,450 = 2*5^2*7*240287
which has 2*3*2*2 = 24 factors and would appear 24 times in a 84,100,450x84,100,450 multiplication table.

Posted by Jer on 2012-12-11 12:59:39