# zbMATH — the first resource for mathematics

Another simple construction of Smith numbers. (English) Zbl 1209.11017
Let $$S(n)$$ be the sum of digits of the natural number $$n$$, $$S_p(n)$$ the sum of the sum of digits of the prime factors of $$n$$, counting multiplicity. A composite number $$n$$ is called a Smith number if $$S(n)=S_p(n)$$. The author proves that for any prime $$P>5$$ with $$S(P)=5$$, the numbers $$21P$$ and $$112P$$ are Smith numbers.
##### MSC:
 11A63 Radix representation; digital problems 11A41 Primes
##### Keywords:
sum of digits; Smith numbers