Finding Sigma(12^12) - Number Theory

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SUMMARY

The discussion focuses on calculating sigma(12^12), where sigma(n) represents the sum of the positive divisors of n. The value of n is expressed as 12^12, which can be factored into (3^12)(2^24). The formula used to compute sigma(12^12) is sigma(12^12) = (1-2^25)/(1-2) * (1-3^13)/(1-3), effectively utilizing the properties of prime factorization and divisor functions in number theory.

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AH05
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Let n=12^12. Find sigma(n).

sigma(n) = the sum of the positive divisors of n.
 
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AH05 said:
Let n=12^12. Find sigma(n).

sigma(n) = the sum of the positive divisors of n.

Okay- your serve! What have you done on this yourself?
 
Well, I set it up:

12^12 = (3^12)(4^12) = (3^12)(2^24)

sigma(12^12) = (1-2^25)/(1-2) * (1-3^13)/(1-3)
 

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