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 "10" and 1 + 0 = 1. All numbers whose base "b" digit sum divides "b"−1 is a harshad number in base "b". For a prime number to also be a harshad number, it must be less than or equal to the base number. Otherwise, the digits of the prime will add up to a number that is more than 1 but less than the prime and, obviously, it will not be divisible. For example: 11 is not harshad in base 10 because the sum of its digits "11" is 1 + 1 = 2, and 11 is not divisible