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.
I'm a graduate student in physics. My recent effort is on understanding the solutions of \(\partial_t^2 \psi - \nabla^2\psi + \psi(\psi\psi^* - \psi_0(t)\psi_0^*(t))=0\). But of course I'm open to be distracted by other good maths. #introduction
@christianp thanks again for sharing your fork! I compiled and deployed christianp/mathstodon-3.5.3 on physics.social but now I'm getting an error "Refused to apply inline style because it violates the following Content Security Policy directive: "style-src 'self' 'unsafe-inline' 'nonce-OQqMqadIqohsc6(...)" I found this related thread: https://mathstodon.xyz/@christianp/105978238936720816, do you know if there are any steps I need to take to make it work on my end? Thank you so much for your help!
@j824h huh good to know.. how does arxiv-vanity deal with this limitation?
@j824h indeed, I was not planning to parse the PDF, that seems like a tedious route
@ummjackson very cool, I'll keep an eye out for it! Thanks for the tip I'll check it out.
@threedudesdad what if it's spelled "catsup"? I know it's the exact same thing but for some reason I always expect something a little more fancy
@balloob ooo nice congrats!! Fun random related note, we almost bought a Philips Hue Bridge but then @basnijholt told us that the Yellow already has a zigbee receiver 😆 all out Hue lights magically work now!! I'll be asking Santa for a lot of smart home devices this year 🎄
@ummjackson what's fedibrowse?
@nocontexttrek take it as a compliment, people want you to join their team 🤩
My favorite thing about Mastodon is that it feels like we're taking back the internet.. just like how it was back in the 90's: campy and unpolished, but genuine and personal. Also a little bit like a massive moderation disaster waiting to happen. I'm savoring it for as long as it lasts and before all the big ugly banners and ads inadvertently take over 🥹
@story645 I think it makes sense!
RT @GeoPythonConf
We're happy to announce GeoPython 2023, March 06-08 in Basel, Switzerland - the conference for #Python and #Geo
Call for Speakers is now open: https://2023.geopython.net
#python #geospatial
hey #datascience #machinelearning peeps! could you please recommend a Mastodon instance for a new tooter interested in ML and data science?
Asking for a friend! thanks!
In case people haven't seen this yet, there's an "Academics on Mastodon" list on GitHub here: https://nathanlesage.github.io/academics-on-mastodon/
#Academia #Mastodon #Tips
Physicist, pythonista, quantum engineer