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hoax numbers
A composite number the sum of whose digits is equal to the sum of the digits of its distinct prime factors is called hoax number.

For example,    is a hoax number since  .

The first pair, triple, etc. of consecutive hoax numbers starts at 84, 12955, 291090, 9538589, 3541285143, 136063250955, and 253282144742, respectively.

Up to    there are 3183722 hoax numbers.

The smallest primitive Pythagorean triangle with 3 hoax sides is (32880, 4369, 33169).

Note that Smith numbers are defined similarly, but they take into account prime factors multiplicity. Clearly, a squarefree Smith number is also a hoax number.

The smallest 3 × 3 magic square whose entries are hoax numbers is

 202 526 94 166 274 382 454 22 346

Below, the spiral pattern of hoax numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

The first hoax numbers are 22, 58, 84, 85, 94, 136, 160, 166, 202, 234, 250, 265, 274, 308, 319, 336, 346, 355 more terms

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