(This is OEIS A057531.)
Your task
Given a positive integer, \$n\$, find the \$n\$th number where the digit sum equals the number of factors
Explanation
For example, let's take 22:
Its factors are \$[1, 2, 11, 22]\$ (length: 4).
Its digit sum is 4.
This means that it is a number where the digit sum equals the number of factors.
The series
The first few terms of this series are:
\$[1, 2, 11, 22, 36, 84, 101, 152, 156, 170]\$
Test cases
Note: these are 1-indexed. You may use 0-indexing.
Input Output
1 1
2 2
3 11
4 22
5 36
10 170
20 444
30 828
40 1111
50 1548
100 3588
Clarifications
- You may use either 0-indexing or 1-indexing
- The sequence starts from 1, not from 0
- The factors of a number include 1 and the number itself
- Default sequence rules apply - you may output the first \$n\$ terms, or the infinite sequence, or something else
- This is code-golf, so shortest answer in bytes wins!