# Beautiful Numbers

**Number Theory**Level pending

A natural number is said to be *beautiful* of k-type iff it is divisible by \(k\) and its **complete** digit sum is also \(k\).

Find the number of all the 7-type *beautiful* numbers \(a\) such that \(a<10,000\).

**Details and assumptions-**

-By **complete** digit sum, it is meant that the repeated sum of the digits of a number until and unless a single digit number is obtained. As an explicit example, *complete* digit sum of \(897\) is \(6\) (because \(8+9+7=24\) and \(2+4=6\) ).