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# [BQN](https://mlochbaum.github.io/BQN/), 21 bytes<sup>[SBCS](https://github.com/mlochbaum/BQN/blob/master/commentary/sbcs.bqn)</sup>

```
(¬·×-+´·/0=↕⊸|)¨⊸⊔1+↕
```

[Run online!](https://mlochbaum.github.io/BQN/try.html#code=RuKGkCjCrMK3w5ctK8K0wrcvMD3ihpXiirh8KcKo4oq44oqUMSvihpUKCj5GwqggNDnigL8zMuKAvzE24oC/MjnigL8yMw==)

Mostly one big [train](https://mlochbaum.github.io/BQN/doc/train.html) used to find the appropriate group for each number, to be used with [Group](https://mlochbaum.github.io/BQN/doc/group.html) (`⊔`). The combining functions in a train normally have two arguments, but Nothing (`·`) can be used on the left to not pass a left argument. See also [Indices](https://mlochbaum.github.io/BQN/doc/replicate.html#indices) (`/`), and note that Modulus (`|`) is backwards relative to C-like `%`.

```
(¬·×-+´·/0=↕⊸|)¨⊸⊔1+↕
                  1+↕  # One plus range: 1…𝕩
(             )¨       # On each of these (n):
           ↕           #   Range 0…n-1
            ⊸|         #   Remainder dividing into n
         0=            #   Equals zero
       ·/              #   Indices where true: proper divisors
    -+´                #   Sum with initial value -n
  ·×                   #   Sign
 ¬                     #   One minus that
                ⊸⊔     # Use to group 1+↕
```

There might be a better solution based on taking the modulus on all pairs instead of one at a time. `(¬·×-+˝(⊣×≠>|)⌜˜)⊸⊔1+↕` is close at 22 bytes.