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Smith numbers
A Smith number is a composite numbers such that sum of digits of is equal to the sum of digits of the prime factors of , counted with multiplicity. They are also called joke numbers.

For example, 666 is a Smith number since and .

Note that hoax numbers are defined similarly, but they do not take into account prime factors multiplicity. Clearly, a squarefree hoax number is also a Smith number.

The first pair, triple, etc. of consecutive Smith numbers (also called Smith brothers) starts at 728, 73615, 4463535, 15966114, 2050918644, 164736913905, and 8090674745553, respectively.

If the requisite of compositeness is left aside, then all the prime numbers trivially satisfy the condition on the sum of digits and it is possible to find a run of length 9 starting at 1979414080360.

Below, the spiral pattern of Smith numbers up to . See the page on prime numbers for an explanation and links to similar pictures. The smallest 3 × 3 magic square made of Smith numbers is

 202 526 94 166 274 382 454 22 346

The first Smith numbers are 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438 more terms

Smith numbers can also be... (you may click on names or numbers and on + to get more values)