Smith number: composite n where digitSum(n) = sum of digit sums of prime factors (with multiplicity). Named after Harold Smith, whose phone number 493-7775 = 3×5²×65837 satisfies this. First few: 4,22,27,58,85,94.
How to Use
Enter n:
- Check: Is n a Smith number?
- Digit sum: Of n and its factors
- Factors: Prime factorization
Properties
- There are infinitely many Smith numbers
- Smith brothers: consecutive Smith numbers
- k-Smith: digit sum equals k× factor digit sum
History
Albert Wilansky noticed his brother-in-law Harold Smith's phone number 4937775 had this property. The name 'Smith number' stuck after Wilansky published it in 1982.
Step-by-Step Instructions
- 1Enter n.
- 2Check Smith.
- 3View factorization.
- 4Compare digit sums.
- 5Scan range.