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Old 2011-07-26, 19:11   #5
schickel
 
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"Frank <^>"
Dec 2004
CDP Janesville

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Quote:
Originally Posted by JohnFullspeed View Post
0 . 276 = 2^2 * 3 * 23
1 . 396 = 2^2 * 3^2 * 11
2 . 696 = 2^3 * 3 * 29
3 . 1104 = 2^4 * 3 * 23
4 . 1872 = 2^4 * 3^2 * 13

I don't understand how to compute 396 from 276

276 = 2^2 * 3 * 23 the sum of the factos is for me 4+3+23 =30
30 = 2*3*5 sum 10
10= 2*5 sum 7
7=7*1 end of the sequence so the sequands is

276,30,10,7,1 what I forget?

John
What's missing is that we use the divisors of the number, not just the prime divisors of the number.

It might be easier to start with a smaller number. Say we're going to calculate the aliquot sequence for 12. If you plug 12 into Dairo's factorization applet, you get this answer:
Quote:
12 = 2 ^ 2 x 3

Number of divisors: 6

Sum of divisors: 28
As you can see, the prime divisors are 2 & 3, but it says there are 6 divisors. That's becuase the divisors are actually: 1, 2, 3, 4, 6, & 12. The sum is 28, but we subtract the number itself, since we want the aliquot divisors (aliquot divisor being defined as a number that divides the original number, excluding the number itself).

So our sequence start out:
0. 12 = 2^2 * 3

Sum of divisors is 28, 28-12 = 16 so the next line is:
1. 16 = 2^4

The sum of divisors is 1+2+4+8+16 = 32 - 16 (the original number) = 15.

Continuing like this, our next couple of lines are:
2. 15 = 3 * 5
3. 9 = 3^2
4. 4 = 2^2
5. 3=3

And our sequence terminates.

Does this help?
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