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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
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