Recent content by suchith

Of course I have using my computer. I don't remember the result now. I have tried for both. Well! Using computer it is not a big job. 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...

I don't know Double integrals. Is it possible to prove the result only using Single variable calculus? At first I tried Integration by parts, but I failed :( Isn't it possible to integrate using limit of sums and symmetry with suitable manipulations? I tried to sum directly but failed :(

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...

\int^{∞}_{-∞} e^{-x^{2}}dx = \frac{\sqrt{\pi}}{2}

What factors lead to limiting of maximum permissible current besides limit of drift velocity?

Given a large number N, do we have any formula to find the number of prime factors and their sum like τ(N) and σ(N) functions? CONDITION: One should not list the factors of N or is not allowed to factorize N since afterwards it would be just a matter of counting and addition

If we are given a metallic conductor in a given Temperature(Room temperature here), Area of cross section A, is there an upper limit to the strength of the current through such a conductor due to the upper limit for drift velocity(v)?? I=nAve e=electron charge n=electron density