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Duffinian numbers
So called by Richard Duffy who introduced them, they are those composite numbers which have no prime factors in common with the sum of their divisors .

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

 18649 18631 18643 18635 18641 18647 18639 18651 18633

The first Duffinian numbers are 4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, 64, 65, 75, 77, 81, 85, 93, 98, 100 more terms

Duffinian numbers can also be... (you may click on names or numbers and on + to get more values)