Smith number
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed.
| Named after | Harold Smith (brother-in-law of Albert Wilansky) |
|---|---|
| Author of publication | Albert Wilansky |
| Total no. of terms | infinity |
| First terms | 4, 22, 27, 58, 85, 94, 121 |
| OEIS index | A006753 |
Smith numbers were named by Albert Wilansky of Lehigh University, as he noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
- 4937775 = 3 · 5 · 5 · 65837
while
- 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)
in base 10.
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