Marcel,
I've got a couple of problems with the examples on your "Perfect Number
code" webpage:
http://home.iae.nl/users/mhx/perfect.html
You state:
"The perfect number A can be characterized by a unique number n, where A =
2^n * (2^n-1 - 1). "
Given one of the prior numerical examples:
"8,128 = 2^6 * (2^7 - 1)"
I.e., 2^6 is 2^n, so n=6, correct?:
1984 = 2^6 * (2^(6-1) - 1)
1984 = 2^6 * (2^5 - 1)
I see 2^5-1 instead of 2^7-1. Shouldn't the A equation be?:
A = 2^n * (2^(n+1) - 1)
You also state:
"To check A, we must find the sum of all of the divisors of 2^n * (2^n-1 -
1), or, equivalently,
[1] x1 = the sum of the divisors of 2^n
+
[2] x2 = the sum of the divisors of (2^n-1 - 1).
According to Pythagoras, x1 = 2^n-1."
If A=8128, then n=6, so x1=2^6-1 equals 63. Hard to figure how
A=8128=x1+x2
with x1=63... I.e., x2 must be large for A=8128 if x1 is small. But, x2
is
small since x2 is 128, i.e., sum of all divisors of 127. x2=128 is 1 plus
the prime: 127=2^((n=6)+1)-1, correct? Are you sure summing x1 and x2 is
equivalent? Multiplying them doesn't seem to work either...
Rod Pemberton
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