perfect

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.
The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols,




σ

1


(
n
)
=
2
n


{\displaystyle \sigma _{1}(n)=2n}
where




σ

1




{\displaystyle \sigma _{1}}
is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 = 28.
This definition is ancient, appearing as early as Euclid's Elements (VII.22) where it is called τέλειος ἀριθμός (perfect, ideal, or complete number). Euclid also proved a formation rule (IX.36) whereby



q
(
q
+
1
)

/

2


{\displaystyle q(q+1)/2}
is an even perfect number whenever



q


{\displaystyle q}
is a prime of the form




2

p



1


{\displaystyle 2^{p}-1}
for positive integer



p


{\displaystyle p}
—what is now called a Mersenne prime. Two millennia later, Leonhard Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem.
It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist. The first few perfect numbers are 6, 28, 496 and 8128 (sequence A000396 in the OEIS).

You do not have permission to view the full content of this post. Log in or register now.
  1. P

    Help Perfect Money E Wallet

    Baka may alam kayo paano ma wí†hdráw ang pera sa Perfect Money.
  2. J

    Perfect World Manga (2014-2021) and Live Action JPDrama (2019) [Completo]

    Manga and JP Drama Series para kompleto rekados! note: movie 2018 movie adaptation THREAD HERE ngunit "...no longer available" yung Mega link plus other THREAD (JPDrama version) HERE is "...not found" yung files Disclaimer: always remember, ang Manga ay laging malaman' vs live actions...
  3. D

    Help Perfect World VNG

    Baka may old player dito ng Perfect World VNG, S1 po sana looking to buy po ako or baka may gusto mag bigay willing din po ako mag accept ng bigay lang kahit alt haha
  4. D

    Perfect example

  5. B

    Swiss Perfect 98 or Swiss Manager

    Good day mga pops. Baka meron po kayo dyan Swiss Perfect 98 or Swiss Manager full version?
  6. C

    Perfect

  7. C

    Perfect combination

  8. K

    Android App YouCam Perfect - Photo Editor v5.89.0

    Download Size : 134.016 MB YouCam Perfect ρrémíùm APK For Android The best photo studio to make all your pictures even better! Edit photos with mosaic to pixelate photo backgrounds, vignettes, overlays, HDR, etc. Features of the App The best photo studio to make all your pictures even better...
  9. M

    IPTV Perfect Player With M3u na

    Credits to the owner nakita ko lang sa fb share ko din dito
  10. P

    PERFECT SLICE SA CAKE

    Happy Birthday 🥳 Hidden content
  11. T

    Android App Perfect Me MOD APK For v8.6.3 (ρrémíùm Unlocked)

    Perfect Me MOD APK (VIP Unlocked): Your Ultimate Photo Enhancement Solution In today’s age of selfies and instant photography, having the perfect tool to enhance your photos is essential. Enter Perfect Me MOD APK, an AI-powered photo editing application designed to make your selfies and portrait...
  12. C

    Perfect 95 ka sakin iha

  13. L

    Help Pa request ng The Perfect Deal

    Baka meron po kayo ng The Perfect Deal. Korean series po siya. Thanks
  14. R

    Perfect Body

    Ctto. Mukhang Kailangan ko na ulit mag workout hehe
  15. C

    He's so smart

  16. P

    Course [LIMITED] UDEMY PREM'IUM COURSE | HOW TO CHOOSE THE PERFECT DIAMOND FOR YOUR ENGAGEMENT RING | CERTIFICATE GUARANTEED I DEEPMODS

    This course includes: 1.5 hours on-demand video Access on mobile and TV Full lifetime access Certificate of completion What you'll learn What it means to buy a diamond today What are all the steps for purchasing the best diamond engagement ring for your partner and how to best face them Which...
  17. R

    [NSFW] The perfect frame

  18. B

    Tap Scroll - Perfect Scroll

    Tired of frantically swiping up to get back to upper of the page? TapScroll makes it easy to scroll to upper of the page, with just one simple tap: a quick tap at the status bar (upper of the screen) To try this, open an app with a scrolling page, such as a web page, Mail list, or a long...
  19. C

    Very perfect

  20. A

    Help PERFECT PITCH 1, 2, and 3

    baka meron po kayo dyna perfect pitch 1 to 3, pa drop nalang po ng link salamat
  21. S

    The Perfect Animal

    Now that I think about it, I think it's true.
  22. G

    Perfect combination

    🖼️Ctto.
  23. B

    The Perfect Resume

  24. C

    Tutorial Pork Empanada Perfect pang Negosyo

    PS. Improve niyo lang ang palaman kung gusto niyo kumita pa nang mas malaki.
  25. K

    Business Idea

    Diba napaka clever nung nag isip nung donut business.. 🟰 💵 ➕️ 🟰 💵💵 Ano kaya kung...
  26. T

    Help Help! Need to choose a perfect modem

    Hello mga ka phcorner experts jan.. I need your Advice on which on modem fits.. Ask ko lang if alin ba sa mga modem's ang ok bilhin We are actually using only 3 devices in our place, ( 2 Mobile device and a Laptop). I AM LOCATED AT QUEZON CITY (SANDIGAN AREA, NEAR BATASAN HILLS) THANK YOU VERY...
  27. R

    Yup, Perfect Life

    🖼️ Ctto. Rich Cat Si Miming Hahaha
  28. S

    Perfect Illustration

    *Credits to the rightful owner of the photo.
  29. B

    Trivia Wimbledon tennis balls are all stored at perfect room temperature

    Wimbledon tennis balls are all stored at perfect room temperature All Wimbledon tennis balls are kept at 68 degrees Fahrenheit because the temperature of the tennis ball affects how it bounces, and all tennis balls must be kept as consistent as possible for competitive reasons. When the ball...
  30. P

    Trivia Hey atheists, I want you to take 10 deep breaths.

    Each breath you feel the warm, healing energy of God in your lungs. At last, you slowly exhale the 10th time. Are you still an atheist? Disclaimer: The views and opinions expressed in this post are those of the original speakers and do not necessarily reflect the views or positions of the...
  31. M

    Trivia CHATGPT is not accurate!

    Guys, ito lang napansin ko kay chatgpt gumagawa gawa siya ng data sometimes link pag nag ask ka ng references or link if saan galing yung data or info. Kaya mabuti parin i double check natin yung mga info mula sa CHatGpt or in general any info sa internet.
  32. D

    Is the law of God perfect?

    Hidden content
  33. C

    Android App Perfect Piano ( with Music SHEETS!! )

    Perfect Piano is an intelligent piano simulator design for Android phones and tablets. With in-built genuine piano timbre, this app can teach you how to play piano and amuse you at the same time! perfectpiano_v6.8.2

Did you know?

Credit is the trust which allows one party to provide money or resources to another party wherein the second party does not reimburse the first party immediately, but promises either to repay or return those resources at a later date.

Lenders want to make sure all their bases are covered before they extend you credit. That means they may look at factors other than your credit score to determine whether to lend you money. Your employment status also can play a role: If your income is too low or you haven’t been at your current workplace long, those factors could weigh against you.

Errors can come in a variety of forms. You may not have been credited for a payment you made, or you may have been charged for a purchase you didn’t make. A debt might be listed more than once, or your balance might be wrong.
Back
Top