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The existence of infinitely many k-Smith numbers. (English) Zbl 0608.10012
Let m be a positive composite integer, and denote by S(m) the sum of digits of m and by $$S_ p(m)$$ the sum of digits of all prime factors of m. The author calls (for k any positive integer) m a ”k-Smith number” if $$S_ p(m)=k\cdot S(m)$$ and shows that there exist infinitely many k- Smith numbers for each k.
Reviewer: P.Kirschenhofer

##### MSC:
 11A63 Radix representation; digital problems 11B39 Fibonacci and Lucas numbers and polynomials and generalizations
##### Keywords:
sum of digits; Smith number