70 is weird

In math and number theory there are many sequences of numbers and one of the most interesting ones is the weird numbers! In this video, we examine the motivation behind them, especially abundant numbers, deficient numbers, perfect numbers, highly composite numbers, and practical numbers.

#math #70 #numbers

[esotorrent]

Its interesting how we subconciously see numbers as "more or less prime" despite not knowing mathematically why

[mitchellboyce]

Pausing halfway through the video to say this is the first time I've ever seen an explanation of perfect numbers that feels compelling at all. I never understood in what context their usual definition was supposed to matter at all, and this helps it make a lot more sense!

[Micha-Hil]

6
Mathematicians: Beautiful. Elegant. Perfect.

7
Mathematicians: Disgusting. Horrid. Unusable.

[simonwillover]

70 here, and I would like to verify this: I am in fact a bit weird.

[petrxs]

These math vids are insane, as a nerd I ask you to continue making these.

[carloselfrancos]

Thank you so much. You reignited my passion for numbers. Take care!

[minirop]

And I thought 70 was weird because it was just 60 + 10.

[MathFromAlphaToOmega]

Very interesting video! Here are a few of my favorite interesting facts about sums of divisors:

1. Euler found a pretty amazing recursion for σ(n):

σ(n)=σ(n-1)+σ(n-2)-σ(n-5)-σ(n-7)+σ(n-12)+σ(n-15)-σ(n-22)-σ(n-26)+...,
where the signs are +, +, -, -, +, +, -, -, etc. the numbers 1, 2, 5, 7, ... are pentagonal numbers, and we count σ(0) as n if n is a pentagonal number. This comes from his pentagonal number theorem, and a very similar recursion is also valid for the partition function p(n) (the only difference being that p(0) is counted as 1, not n as in the case of σ).

2. The Riemann hypothesis is equivalent to σ(n)<e^γ*nlog(log n) for n>5040, where γ is the Euler-Mascheroni constant.

3. A number satisfying σ(n)=2n+1 is called "quasiperfect", but none are known to exist. It's known that if any do exist, they must be odd squares larger than 10^35.

[omersaid]

Please continue making videos like this. Your views may be low but be sure your videos are very valuable and we know that.

[ErikLeppen]

I love how naturally your story moves towards these practical numbers.

[Kay-qlwl]

I LOVE THIS WAY OF LOOKING AT NUMBERS! It feels like innate truths are being revealed in a way that flimsy addition or subtraction could never manage. And getting to have personlaities, vibes, feelings and characterisations applied to numbers in a rigorous way is anazing

[Kirbysnumberonefan-]

For some reason this has become my comfort video, I’m watching this for the fourth time now

[Lunar-Biohazard]

I should be doing something but instead I'm watching some dude on the internet insult the number 70 in the most overly complicated way imaginable.

[Stack-vccw]

0:35 quest for perfection instantly brought me old gd times back

[jademonas]

the weirdest number for me is 193
but thats only because every single time i bought lunch in college my number to pick up the food at the restaurant it rung up 193

[goodguyamr]

I’m tempted to make up a base-70 numeral system and make people suffer using it

[maradupras]

as an autistic person with a special interest in math i especially like the idea of thinking of numbers as having personalities, so this is a great video for that!! 70 is a Weird Little Child and i love them for it :)

[TheMasonX]

Loved this! Got to learn about several new categories/sequences of numbers and your graphics convey so much meaning and understanding. Thanks for making my Monday, hope yours was great and I'm looking forward to the next video as always!

[AlanHernandez-jgxv]

Your voice is so relaxing, makes me feel calm and safe.
You should make compilation of your videos to fall asleep to

[HM-scto]

I love this! I've watched a lot of math videos and read many pop math books in my day. Many of them talk about perfect numbers (to the point of nausea) and this felt like a fresh take on the subject.