This is from the Wikipedia entry for Field of Sets

"Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly the term "algebra over \(X\)" is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory. "

I came across this nice integerological fact:

Define \(\operatorname{ord}_p(n)\) to be the power of \(p\) in the prime factorisation of \(n\).

Then

\[ \sum_{k=1}^n\gcd(n,k) = \prod_{p|n} \left(1+\left(1-\frac{1}{p}\right) \cdot \operatorname{ord}_p(n)\right) \]

I don't know why you'd want to do this, and all the references I've found to it talk about it as a special case of some more general identities, but for some reason it appealed to me.

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Hiya! I'm Ryn, although that may change at some point. Currently working on my masters thesis in non-distributive modal logic. I hope to make some nice maths friends here!

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Joined Mar 2021