where is a digit of , and is the number of digits of . This means a test of whether the sum of the digits of times the product of the digits of is equal to .
For example, the number 128 in base 7 is a sum-product number since
All sum-product numbers are Harshad numbers, too.
0 and 1 are sum-product numbers in any positional base. The proof that the set of sum-product numbers in base 2 is finite is elementary enough not to inspire claims of authorship. The proof that the set of sum-product numbers in base 10 is finite (specifically, 0, 1, 135 and 144) is more involved but within the realm of basic algebra, and it points the way to a formulation of the proof that number of sum-product numbers in any base is finite.
|Date of creation||2013-03-22 15:46:50|
|Last modified on||2013-03-22 15:46:50|
|Last modified by||Mravinci (12996)|
|Synonym||sum product number|