# Sum-product Numbers

A **sum-product number** is an integer that in a given base is equal to the sum of its digits times the product of its digits. Or, to put it algebraically, given an integer *n* that is *l* digits long in base *b* (with *d**x* representing the *x*th digit), if

then *n* is a sum-product number in base *b*. In base 10, the only sum-product numbers are 0, 1, 135, 144 (sequence A038369 in the OEIS).

Thus, for example, 144 is a sum-product number because 1 + 4 + 4 = 9, and 1 × 4 × 4 = 16, and 9 × 16 = 144.

Write a program in a C language that will find it and display all the numbers that meet the above property and are less than 1000. In the end, their crowd should also be displayed.