# 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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