PERFECT NUMBERS ???

[DINI]

Hi,

Define "Perfect number".
give examples.

Dini.

[Paul McKenzie]

A perfect number is a number whose sum of
all of its divisors (except for the number) is
equal to the number itself.

Example: 6 = (1+2+3).

I leave it as an exercise for you to come up with
the next 3.

Regards,

Paul McKenzie

[Mallik Bulusu]

the generic formula for a perfect number is as below:
every number of type (2 power n)*((2 power (n+1) - 1) is a perfect number if
((2 power (n+1) - 1).


Let us say :
T1 = 2 power n
T2 = 2 power (n+1) - 1

i.e T1 = 2 * 2 * 2 * ........ n times.
and T2 = T1 * 2 -1


if T2 is a prime number, then product of T1 and T2 is a perfect number.

Examples of T2 to be prime numebers


n = 1, T2 = 3 prime => 2*3 = 6 is a perfect number.
n=2 , T2 = 7 prime => 4*7 = 28 is a perfect number.
n=4, T2= 31 prime => 16*31 = 496 is a perfect number.
where as
n=3, T2 = 15 in not a prime => 8*15 is not a perfect number.