HarshadNumbers

The Harshad (Niven) numbers $1, 2, 3, …, 10, 12, 18, …$ : integers divisible by their own digit sum.

HarshadNumbersthe

n

with

n \bmod \mathrm{digitSum}(n) = 0

, an infinite indexed collection.

Domain: Collections

Details

A lazy indexed collection: $Count(HarshadNumbers) = +\infty$ -- every digit-sum-1 number (a power of 10) qualifies, so the family never thins out. OEIS A005349.
$At(HarshadNumbers, k)$ unranks by scanning forward from the last cached match -- $At(HarshadNumbers, 11) = 12$ .
Membership goes through Element: $Element(18, HarshadNumbers)$ is true (digit sum 9, $18/9=2$ ), $Element(11, HarshadNumbers)$ is false.

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS