Harshad number
When an integer is divisible by the sum of its digits, it’s called a Harshad number or Niven number. That is, given m is the number of digits of n and d is an integer of n,
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).
| Title | Harshad number |
|---|---|
| Canonical name | HarshadNumber |
| Date of creation | 2013-03-22 15:47:04 |
| Last modified on | 2013-03-22 15:47:04 |
| Owner | PrimeFan (13766) |
| Last modified by | PrimeFan (13766) |
| Numerical id | 5 |
| Author | PrimeFan (13766) |
| Entry type | Definition |
| Classification | msc 11A63 |
| Synonym | Niven number |
| Defines | Harshad number |