6, 12

12 (number)

12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...

, 18

18 (number)

18 is the natural number following 17 and preceding 19.In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is stressed: 18 vs 80 . However, in dates such as 1864, or when contrasting numbers in the teens, such as 17, 18, 19, the stress...

, 20

20 (number)

20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....

, 24

24 (number)

24 is the natural number following 23 and preceding 25.The SI prefix for 1024 is yotta , and for 10−24 yocto...

, 28

28 (number)

28 is the natural number following 27 and preceding 29.-In mathematics:It is a composite number, its proper divisors being 1, 2, 4, 7, and 14....

, 30

30 (number)

30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....

, 36

36 (number)

36 is the natural number following 35 and preceding 37.- In mathematics :36 is both the square of 6 and a triangular number, making it a square triangular number...

, 40

40 (number)

40 is the natural number following 39 and preceding 41.Despite being related to the word "four" , 40 is spelled "forty", and not "fourty"...

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Properties

• Every multiple of a semiperfect number is semiperfect. A semiperfect number that is not divisible by any smaller semiperfect number is a primitive semiperfect number
  Primitive semiperfect number
  In number theory, a primitive semiperfect number is a semiperfect number that has no semiperfect proper divisor....
  
  .
• Every number of the form 2^mp for a natural number m and a prime number
  Prime number
  A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
  
   p such that p < 2^{m + 1} is also semiperfect.
  • In particular, every number of the form 2^m-1(2^m-1) is semiperfect, and indeed perfect if 2^m-1 is a Mersenne prime
    Mersenne prime
    In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
    
    .
• The smallest odd semiperfect number is 945 (see, e.g., Friedman 1993).
• A semiperfect number is necessarily either perfect or abundant. An abundant number that is not semiperfect is called a weird number
  Weird number
  In number theory, a weird number is a natural number that is abundant but not semiperfect.In other words, the sum of the proper divisors of the number is greater than the number, but no subset of those divisors sums to the number itself.- Examples :The smallest weird number is 70...
  
  .
• With the exception of 2, all primary pseudoperfect numbers are semiperfect.
• Every practical number
  Practical number
  In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n...
  
  that is not a power of two is semiperfect.