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 \(2+4=6\) ).


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