Consider the integer 1729. Adding up its digits,
All 1-digit numbers and the base number itself are Harshad numbers. 1, 2, 4 and 6 are always Harshad numbers regardless of the base.
It is possible for an integer to be divisible by its digital root and yet not be a Harshad number because it doesn’t divide its first digit sum evenly (for example, 38 in base 10 has digital root 2 but is not divisible by 3 + 8 = 11). The reverse is also possible (for example, 195 is divisible by 1 + 9 + 5 = 15, but not by its digital root 4).
|Date of creation||2013-03-22 15:47:04|
|Last modified on||2013-03-22 15:47:04|
|Last modified by||PrimeFan (13766)|