Thread: Odd numbers

Is anybody here familiar with numbers like perfect numbers, perfect prime numbers or friendshipnumbers?
I find them utterly fascinating.

I know some basic things about even perfect numbers, and I'm assuming by perfect prime numbers you mean Mersenne primes, in which case I know about the relationship between these and even perfect numbers. I don't know about friendship (friendly?) numbers, but they seem to involve the divisor function, about which I know quite a bit.

Perfect prime numbers are prime numbers which continue to be primes even if you scramble the numbers they consist of.
For instance 13
13 31
or 373.
Friendly numbers work in pairs
Say that we have to numbers, b & c.
If the sum of c's divisors equals b and vice versa b and c form a pair of friendly numbers.

Let me tell you about the perfect number a perfect number can be defined as an integer, which is a non-zero number. A perfect number can be obtained by adding all the factors which are less than that number. All perfect numbers are even. There is no odd perfect number.perfect number is a whole number in which the term itself is equal to the sum of all its factors.