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(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!

I have some Python solutions that I'll post in a few days if they don't get beaten:

• 88 bytes for the infinite sequence
• 92 bytes for the \$n\$^th term
• 126 bytes for the first \$n\$ terms

• Mukundan314 came up with an 80-byte solution
• Arnauld came up witha 78-byte solution

(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!

(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!

I have some Python solutions that I'll post in a few days if they don't get beaten:

(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!

I have some Python solutions that I'll post in a few days if they don't get beaten:

• 88 bytes for the infinite sequence
• 92 bytes for the \$n\$^th term
• 126 bytes for the first \$n\$ terms

• Mukundan314 came up with an 80-byte solution
• Arnauld came up witha 78-byte solution

(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!

(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!

I have some Python solutions that I'll post in a few days if they don't get beaten:

• 88 bytes for the infinite sequence
• 92 bytes for the \$n\$^th term
• 126 bytes for the first \$n\$ terms