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# [BQN](https://mlochbaum.github.io/BQN/), 25 bytes<sup>[SBCS](https://github.com/mlochbaum/BQN/blob/master/commentary/sbcs.bqn)</sup>

```
⌊⊸≡(/0=↕⊸|){(+´÷≠)∘𝔽¨«⟜𝔽}
```

[Run online!](https://mlochbaum.github.io/BQN/try.html#code=UkMg4oaQIOKMiuKKuOKJoSgvMD3ihpXiirh8KXsoK8K0w7fiiaAp4oiY8J2UvcKowqvin5zwnZS9fQoK4omN4p+cKFJDwqgpIDHigL8z4oC/NeKAvzEw4oC/MTXigL8yMDbigL8yMDc=)

This expression has a complicated structure. [This link](https://mlochbaum.github.io/BQN/try.html#code=4oyK4oq44omhKC8wPeKGleKKuHwpeygrwrTDt+KJoCniiJjwnZS9wqjCq+KfnPCdlL19&explain) uses BQN's explain feature to show the order in which everything is applied. It's split into two expressions, where the `{` on the left indicates to apply the modifier on the right.

```
⌊⊸≡(/0=↕⊸|){(+´÷≠)∘𝔽¨«⟜𝔽}
   (/0=↕⊸|){            }  # Operand 𝔽 to block modifier: proper divisors
       ↕                   #   Range 0,…,n-1
        ⊸|                 #   before modular division
     0=                    #   equals zero
    /                      #   Indices of ones
                       𝔽   # Apply the operand
                     «⟜    # Shift in the number itself
                    ¨      # On each divisor:
                  ∘𝔽       #   Apply the operand again, then
            (+´÷≠)         #     Mean (sum divided by length)
⌊⊸≡                        # Floor matches argument
```

Much of the structure is composed of [Before and After](https://mlochbaum.github.io/BQN/tutorial/combinator.html#before-and-after) (`⊸⟜`) and [trains](https://mlochbaum.github.io/BQN/doc/train.html), with one [block modifier](https://mlochbaum.github.io/BQN/doc/block.html#operands). The function `/0=↕⊸|` gives proper divisors including 1, but for testing which divisors are cool we want to include the number itself and exclude 1 (we know it's cool). [Shifting](https://mlochbaum.github.io/BQN/doc/shift.html) in the original number on the right side accomplishes this.