## Definition

A harshad number is a positive integer which is divisible by the sum of its digits base $10$.

Hence a harshad number is a Niven number base $10$.

## Sequence of Harshad Numbers

The sequence of harshad numbers begins:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, \ldots$

## Also see

• Results about harshad numbers can be found here.

## Historical Note

Harshad numbers were first described by Dattathreya Ramchandra Kaprekar.

## Linguistic Note

The term harshad number comes from the Sanskrit word हर्ष (harṣa + da), which means giving joy.