A number is called sN if it is divisible not only by the sum of its digits (like Harshad numbers) but also by the sum of any subset of its (nonzero) digits.

For example, the number 68040 is sN because it is divisible by 6, 8, 4, 6+8, 6+4, 4+8 and 6+4+8.

If    is sN, then clearly also    is sN. The primitive sN numbers are those such that    is not sN.

It is easy to see that there are infinite primitive sN, because all the numbers of the form    are sN, being divisible by 1, 2, and 1 + 2 = 3.

The first super Niven numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 48, 50, 60, 70, 80, 90, 100, 102, 110, 120, 140, 150, 200, 204, 210, 220, 240, 280, 300, 306, 330, 360, 400, 408, 420, 440, 480, 500 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many super Niven numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.