Search a number
weird numbers
A number    is called weird if it is abundant but not pseudoperfect, i.e., if the sum of its proper divisors is larger than  , but there is not a subset of them whose sum is  .

For example, 70, whose proper divisors are 1, 2, 5, 7, 10, 14, and 35 is abundant since

but it not possible to obtain 70 adding a subset of them.

There are infinite weird numbers and S. Benkowski and P. ErdÃ¶s have proved that their asymptotic density is positive.

According to Wenjie Fang, there are no odd weird numbers below  .

Every even number greater than 11634 can be written as the sum of weird numbers.

Sidney Kravitz has proved that, if  ,    is a prime, and

is prime, then    is weird.

The first weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870 more terms

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