1 | initial version |

This seems more like a homework question than something about Sage. Sage won't be able to give you a formula for the number of zero divisors of Z mod (p*q*r) (although one exists); you need some more theoretical knowledge for that. However, here is a naive function which counts the number of zero divisors of Z mod n:

```
def number_of_zero_divisors(n):
zero_divisors = 0
for i in range(1, n):
for j in range(1, n):
if (i*j) % n == 0:
zero_divisors += 1
break
return zero_divisors
```

Here is some sample output:

```
sage: number_of_zero_divisors(2*3*5)
21
sage: number_of_zero_divisors(5*7*11)
144
```

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