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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
File Type: pdf Tau.pdf (180.1 KB, 8 views)
File Type: pdf Sigma Function.pdf (133.5 KB, 7 views)
File Type: pdf The Mobius Function.pdf (126.4 KB, 9 views)
File Type: pdf EulerPhiFunction.pdf (171.0 KB, 8 views)
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January 11th, 2014, 08:06 AM   #2
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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., for (m, n) = 1, of course. This easily proves the conclusion of tau (or, more conveniently, divisor) function too.
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January 12th, 2014, 03:13 AM   #3
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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.
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