|Mar22-13, 06:43 AM||#1|
Sum of number of divisors of first N natural numbers
If σ(N) is the sum of all the divisors of N and τ(N) is the number of divisors of N then what is the sum of sum of all the divisors of first N natural numbers and the sum of the number of divisors of first N natural numbers?
Is there any relation between σ(N) and τ(N) functions?
Can I do that without factorizing any of the number in the sequence?
|Mar22-13, 07:10 AM||#2|
Have you tried calculating those yourself up to, say, N= 100?
|Mar22-13, 11:27 AM||#3|
But can I find it out without listing the factors or factorizing individual numbers?
Avoiding factorization is the goal. I wrote these functions in the form of series, for sum of tau function in the form of infinite series without factorization, and for sum of sigma function it is a finite series. I have written the proof by myself, but don't know about the correctness. Is there anything to find the sum in the mathematical literature?
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