Smith number

A composite number, the sum of whose digits equals the sum of the digits of its prime factors. The name stems from a phone call in 1984 by the mathematician Albert Wilansky to his brother-in-law, called Smith, during which Wilansky noticed that the phone number, 4937775, obeyed the condition just mentioned. Specifically:

4937775 = 3 × 5 × 5 × 65837
4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7

Trivially, all prime numbers have this property, so they are excluded. The Smith numbers less than 1000 are:

4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, and 985.

In 1987, Wayne McDaniel proved that there are infinitely many Smiths.

Related category

• TYPES OF NUMBERS

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