Re: why there are no Odd Perfect Numbers (not including 1) Re:


Gerry Myerson wrote:
> In article <In2HEF.D8u@xxxxxx>, "*** T. Winter" <***.Winter@xxxxxx>
> wrote:
>
> > Wrong. Take 945. The sum of its proper divisors is 975, or about 103 %
> > of the original number. Or take 33426748355, the sum of the proper
> > divisors is 33459293244 (if I did do my calculations correctly)
>
> 33426748355 is not a square (no square ends in 55), so it has an even
> number of divisors, so an odd number of proper divisors, and they're
> all odd, so their sum is odd, so it can't be 33459293244.

Dammit, I gotta know!

C:\python23\user>factor! 33426748355
PRIME_FACTOR 5
PRIME_FACTOR 7
PRIME_FACTOR 11
PRIME_FACTOR 13
PRIME_FACTOR 17
PRIME_FACTOR 19
PRIME_FACTOR 23
PRIME_FACTOR 29
PRIME_FACTOR 31



proper_divisors = []
for a in [1,5]:
for b in [1,7]:
for c in [1,11]:
for d in [1,13]:
for e in [1,17]:
for f in [1,19]:
for g in [1,23]:
for h in [1,29]:
for i in [1,31]:

proper_divisors.append(a*b*c*d*e*f*g*h*i)

proper_divisors.remove(33426748355)
print sum(proper_divisors)

Output:

33459293245

That's better. It was off by 1.

.

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