Persistence of a number assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest
Harshad number "n", and for an odd integer "n" > 1, all positive integers are Nivenmorphic numbers for base "n". e.g. the Nivenmorphic numbers in base 12 are (all positive integers except 13). The smallest number with base 10 digit sum "n" and terminates "n" written in base 10 are: (0 if no such number exists) defines a multiple harshad number as a harshad number that, when divided by the sum of its digits, produces another harshad number. He states that 6804 is "MHN-4" on the grounds that and went on to show that 2016502858579884466176 is MHN-12. The number 10080000000000 = 1008·10,