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January 11th, 2014, 04:16 AM   #1
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Derivation of tau function, sigma, euler and mobius function

I am interested in deriving the formula of four number theoretic functions.To those who will get to see these, kindly check my work (attached pdf) and do comment on them. Your opinions and suggestions are greatly appreciated. There will be more future posts about number theoretic functions and I hope you will not get tired answering my queries. Thanks.
Attached Files
 Tau.pdf (180.1 KB, 8 views) Sigma Function.pdf (133.5 KB, 7 views) The Mobius Function.pdf (126.4 KB, 9 views) EulerPhiFunction.pdf (171.0 KB, 8 views)

 January 11th, 2014, 08:06 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Derivation of tau function, sigma, euler and mobius func Except the conclusion on totient everything seems correct (I haven't dived deeper in the derivation, so I will have to take your word that you haven't done any algebra mistake). For the sigma function, I presume n is a prime power, otherwise that doesn't make sense. Assuming so, definitely more is true and everything can be derived from the fact that it is multiplicative, i.e., $^{\sigma_k(mn)= \sigma_k(m)\sigma_k(n)}$ for (m, n) = 1, of course. This easily proves the conclusion of tau (or, more conveniently, divisor) function too.
 January 12th, 2014, 03:13 AM #3 Newbie   Joined: Jan 2014 Posts: 10 Thanks: 0 Re: Derivation of tau function, sigma, euler and mobius func yes,i've seen it too.thanks and yes for sigma function,n is a prime power.,i'm a bit worried about the mobius function anyway.,is it ok to assume that if n=pq then ?_(d/pq)(?(d))-?_(d/p)(?(d))-?_(d/q)(?(d)), 1 is not included.,though 1 divides pq.

 Tags derivation, euler, function, mobius, sigma, tau

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# conclusion of sigma function

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