For example, 35 is Duffinian since it is relatively prime to the sum of its divisors 1 + 5 + 7 + 35 = 48.
It is easy to see that there are infinite such numbers. Indeed any number of the form where is prime and is Duffinian, since cannot be divisible by .
P. Heichelheim proved that exists a run of 5 consecutive Duffinian numbers starting at 202605639573839041, and that cannot exist a longer such run.
Rose Mary Zbiek has proved that every even Duffinian number is either a square or twice a square.
The smallest 3 × 3 magic square whose entries are consecutive Duffinian numbers is