13 Special Types of Numbers With Strange Names

[@TheRenaSystem]

Just binged every vid on your channel, I am so here for all of it! Not sure if it's the cool educational content, the hilarious edit and set, or your untouchably sublime enthusiasm, but you've reinvigorated my desire to start self educating again, thanks!

[@unclegardener]

Same here.

[@JazzyFizzleDrummers]

🟥⬛️

[@DecayedPony]

I wish I saw stuff like this when I was younger. Would've actually gotten me interested in learning / school.

[@josephrissler9847]

This exactly how I feel. Every time I watch a video from this channel I just smile as I rediscover a love some bit of mathematics and often learn something new. Even when I hear something I already know, I love hearing it again from Professor Domotro. His enthusiasm is contagious.

[@viennaorange4122]

Oddly hypnotized by the smooth and clean shifting of dice into equal piles at 2:15

[@TetrisMaster512]

One thing that I think is kinda interesting about the powers of two being almost perfect numbers, is that you can see this reflected in binary. Like 1000 - 1 = 0111, the result contains every lesser power of two, all of its factors, added together. As an aside, the "power of two minus one" is often used as a trick with programming, replacing a power of two modulo with a cheap bitwise AND operation with the minus one result. I don't know enough about how bitwise (finite field?) arithmetic relates to more general arithmetic to know whether this trick relates to the powers of two being almost perfect.

[@TheBoshy]

Deeply respect the cut aways for each number. Remember us when you at the top of Mathtube.

[@realNom2mooncow]

The cutaways to show what you think each of the numbers' names feel like was great lol. Watching you nod next to the social numbers all piled up in a stack cracked me up

[@stefanfincken4359]

Man this is great! This is how they should teach it in schools. I would have been hooked at a younger age, I'm pretty sure.

[@derekhasabrain]

Dude I’m a math hobbyist and you’ve covered everything I’ve learned ever. I can’t wait to see what else there is to blow my mind

[@someknave]

When you mentioned quasi perfect and almost perfect numbers that made me think about the parity of an aliquot sum. The divisors of a number come in pairs, except for square numbers which have one unmatched divisor, we don't count the number itself though. Odd numbers only have odd factors so odd nonsquares have an odd number of odd proper divisors, and therefore an odd aliquot sum. Odd squares have an even aliquot sum. Even numbers have a number of even divisors which don't affect the parity of the sum, but their odd divisors are the same as the number of divisors of the largest odd divisor (the odd number that you multiply by a power of 2 to get the original number). And then the same logic as above works but flipped because that largest odd divisor is included in the sum. So even numbers will have an odd aliquot sum if and only if their largest odd divisor is a square.

[@usernameisamyth]

You sound like my next favourite KZbinr 🫡 Great video, btw The only other thing that I expected is the pattern of the last digits: 6,8,6,8,... And my most favourite thing about perfect numbers is Euler's (~2000 years old) proof of every even perfect number being of Euclid's form ((2^n-1)•2^(n-1)) Looking forward to your new videos ☺️

[@ComboClass]

Thanks I appreciate it!!

[@utkarshraj9422]

Bro this channel needs instant recognition

[@laz001]

Hey man - love your channel! Just a suggestion - put in mini pauses between sections with the music playing and no discussion, to allow us a moment to take in everything you’ve covered!

[@juniperbelmont]

This was great! Thank you for making these videos.

[@brick4667]

Such a dope idea for a video… really great content

[@ranonrat6164]

really cool to see this kind of content on youtube, thanks for making this kind of content

[@takeguess]

Gotta say you are one of the first channels that I "rang the bell"... You rock.

[@-41337]

speaking of your own "silly names", your distinction of arbitrarily large vs infinite has changed my life. can't believe i've never seen it before. Thank you for that. I hope that important distinction catches on in common usage. I already see threeven.

[@ComboClass]

To clarify, I didn't invent the term "arbitrarily large", which is used in some branches of math, but hopefully I helped popularize it in general life! And yes threeven is very useful haha.

[@mightyboole]

great video. ur gonna make it big dude :)

[@stevenlubick2689]

This was perfect😃😃👍👍

[@dj_enby]

best channel!!!

[@casualcommenter9730]

Could you have an irrational aliquot sequence? Where the quasi looping properities nexessitate an unendibg sequence?

[@gregsarnecki7581]

5:27: It just so happens that 945 is the ratio of pi^6 to zeta(6), i.e. Z(6) = (pi^6)/945.

[@qy9MC]

Honestly this is inspiring

[@УэстернСпай]

The dice randomly flying out of your sleeves killed me 🤣😆

[@aaronclark2599]

Ever done a collab with the Klein bottle collector from Numberphile?

[@theoneandonlymastertroller]

what song do you use in the background

[@thatssokwekwe]

I literally said “please don’t” out loud when he raised that box 1:00

[@brainboy53]

If there is any uncontainable numbers, then there is an infinite!

[@shruggzdastr8-facedclown]

How about taxi cab numbers: Numbers which can be broken down into two different summed pairs of perfect cube numbers -- "1729" being the smallest known example (e.g.: 10^3 + 9^3, and 12^3 + 1^3)?

[@MeriaDuck]

I of course know about primes since prime school I guess (had to make that pun, sorry). Know about Mersenne primes since like the nineties, but I never knew the relation between them and perfect numbers. That's awesome!

[@renovatioimperii9205]

a part 2 for Halloween could be fun if we mention stuff like vampire numbers for example sadly that's the only name i got as of rn though... 😕

[@romeolz]

Oh my god I'm getting 3x+1 flashbacks

[@УэстернСпай]

Me too..

[@joefarrow1599]

If triangle numbers are n(n+1)/2, and (even) perfect numbers are triangled Mersenne primes, what do we get if we triangle a non-Mersenne prime? i.e. a number of the form p(p+1)/2 for p prime such that p eq 2^n-1 ? Does such a number have any interesting properties?

[@somedooby]

I have a love-hate relationship with aliquot sums... They're cool, but kinda hard to compute for large numbers

[@lamonica9202]

this man is underrated

[@angusmacdonald4860]

Sub'd!

[@ludvercz]

I had to rewatch the definition because I kept picturing Aloquatzum as a cool Mesoamerican deity

[@JonathanRuchlis]

Like it love it gotta have it

[@braznartn5176]

You Domotro are... KOOL.

[@EvanEscher]

I'm confused about multi-perfect numbers. How come for perfect numbers, you take the sum of the divisors (not including the number itself), but for multi-perfect numbers, you take the sum of the divisors, but include the number itself?

[@ComboClass]

Perfect numbers can be defined as 2-perfect numbers because perfect numbers can either be defined as their sum without themselves equaling themselves or as their sum including themselves equaling twice themselves (which are equivalent).

[@codatheseus5060]

12-13 min reminded me of the 3n+1 thingy

[@marshallharden5329]

Are you going to clean up all of those dice?

[@ComboClass]

Haha nah, when it rains they get embedded into the dirt ground and become part of the floor and I like how it looks

[@alexgarza3631]

@@ComboClass how many die tho

[@ComboClass]

@@alexgarza3631 Not sure how many were in the box, but I have a total of about 1500 dice in that zone

[@realNom2mooncow]

@@ComboClass it is quarantined from humanity for our own good. The dice zone

[@greego5952]

i like how you thought he cleans his filming area. Very funny.

[@karkavwi]

Researching about such groups of numbers is fascinating. However, are there applications of such types of numbers? If not, then is it wrong to try and research about such numbers?

[@IAmSneak]

It's never wrong to learn more about our world. But how would we even know if there are applications for something? Maybe there's an application for it we've never even thought of!

[@brainboy53]

I’m 70. A weird introvert. (Not 70 years old. I’m only 14)

[@mattt.4395]

so for a square number, would i have to add the square root twice? would the aliquot sum be 1+2? or 1+2+2? and for 8, would it be 1+2+4? or 1+2+2+4? for 9, would it be 1+3? or 1+3+3? imo, it kind of intuitively doesn't make sense to only add it once and not twice. 2 and 8 multiply to 16, and are both included in the aliquot sum (not either-or, but both 2 AND 8). 4 and 4 also multiply to 16, so wouldnt it make sense that they are BOTH included instead of just one of them?

[@solveforx314]

You would only add it once. The aliquot sum is the sum of the proper factors of the number, and 4 is only a factor of 16 once. Hope that helps!

[@NigelTheMini]

Were StandUpMaths and VSauce2 involved in this video? Because I'm here for it!

[@ComboClass]

I’d love to collaborate with Matt Parker (StandUpMaths) or the VSauce guys someday, they’re great

[@brainboy53]

I thought it was 315 5:24 !!?!?!

[@eyesicecold]

315 1,3,5,7,9,15,21,35,45,63,105 1+3+5+7+9+15+21+35+45+63+105=309 Unfortunately not

[@aaronclark2599]

Maybe numbers like 138 that seem to blow up big but then fizzle out and crash could be "trendy" or "fad" numbers?

[@lusr2923]

13:56

[@Air4swan]

Man, my beloved powers of 2 have to settle for being “almost perfect”. I guess that’s still pretty good

[@Very.Crazy.Math.Pistols]

Nice that 1 Is highly composite, but ... not composite. But not prime xD

[@melody3741]

The Alucard numbers are absolutely begging to be made into a fractal I must see it

[@melody3741]

I just realized that this is impossible and I'm incredibly sad about it

[@WhaleCatWhaleCat]

If quasi-perfect numbers are one more then perfect numbers and are odd, then perfect numbers must be a odd number- 1 which is an even number, and so there cannot be a odd perfect number since then the quasiperfect number will be even, which is impossible

[@ComboClass]

That would just show that the perfect number right under that specific quasiperfect number would be even, not that every perfect number would have to be (which is still unknown)

[@willoeters9681]

Why didn’t he mention that not only is 6 a perfect number it’s factors 1,2,3 multiply to make 6 making it really special

[@emilyrln]

It's nice that 70 is the first weird number 😂

[@pepebriguglio6125]

So, so far sublime numbers have either 2 or 77 digits ...🤔🤔🤔... So, no sublime numbers with 6 or 28 digits, I suppose ...🤔🤔... But ☝️🤓... Wouldn't it be cool, if sublime numbers with 496 or 8128 digits exist. If they do, then I would already now like to name them 'triblime numbers' 😎

[@angelmendez-rivera351]

Interestingly, 1 has no proper divisors. This is why 1 is not a prime number.

[@mattt.4395]

today i learned: numbers have periods. next episode: menopausal numbers

[@SuryaBudimansyah]

All you need is a proper English subtitle

[@johnloony68]

globule

[@SHOSHO510]

Haha … I’ve got your number 🙃

[@coktatlveiyidirkahramankag5893]

I forgor