To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Primitive abundant number

From Wikipedia, the free encyclopedia

In mathematics a primitive abundant number is an abundant number whose proper divisors are all deficient numbers.[1][2]

For example, 20 is a primitive abundant number because:

  1. The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number.
  2. The sums of the proper divisors of 1, 2, 4, 5 and 10 are 0, 1, 3, 1 and 8 respectively, so each of these numbers is a deficient number.

The first few primitive abundant numbers are:

20, 70, 88, 104, 272, 304, 368, 464, 550, 572 ... (sequence A071395 in the OEIS)

The smallest odd primitive abundant number is 945.

A variant definition is abundant numbers having no abundant proper divisor (sequence A091191 in the OEIS). It starts:

12, 18, 20, 30, 42, 56, 66, 70, 78, 88, 102, 104, 114

YouTube Encyclopedic

  • 1/3
    33 537
    1 203 966
    892 985
  • ✪ 60,000 year old Genetic "Reset Device" ? Pandora's box, Ark of the Covenent, "Ark of Noah"
  • ✪ Should We Build a Dyson Sphere? | Space Time | PBS Digital Studios
  • ✪ Life Begins: Crash Course Big History #4



Every multiple of a primitive abundant number is an abundant number.

Every abundant number is a multiple of a primitive abundant number or a multiple of a perfect number.

Every primitive abundant number is either a primitive semiperfect number or a weird number.

There are an infinite number of primitive abundant numbers.

The number of primitive abundant numbers less than or equal to n is [3]


  1. ^ Weisstein, Eric W. "Primitive Abundant Number". MathWorld.
  2. ^ Erdős adopts a wider definition that requires a primitive abundant number to be not deficient, but not necessarily abundant (Erdős, Surányi and Guiduli. Topics in the Theory of Numbers p214. Springer 2003.). The Erdős definition allows perfect numbers to be primitive abundant numbers too.
  3. ^ Paul Erdős, Journal of the London Mathematical Society 9 (1934) 278–282.

This page was last edited on 17 May 2019, at 17:17
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.