Difference between revisions of "Manuals/calci/PERFECTNUMBERS"
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*Perfect number is a positive integer which is equal to the sum of its proper divisors. | *Perfect number is a positive integer which is equal to the sum of its proper divisors. | ||
*The smallest perfect number is 6, which is the sum of 1, 2, and 3. | *The smallest perfect number is 6, which is the sum of 1, 2, and 3. | ||
| + | |||
| + | ==ABUNDANTNUMBERS== | ||
| + | *Abundant number is a number for which the sum of its proper divisors is greater than the number itself. | ||
| + | *It is also called Excessive Number. | ||
| + | *The first Abundant number is 12. | ||
| + | * Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. | ||
| + | *The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4. | ||
| + | *ABUNDANTNUMBERS(110) = 12 18 20 24 30 36 40 42 48 54 56 60 66 70 72 78 80 84 88 90 96 100 102 104 108 | ||
| + | |||
| + | ==DEFICIENTNUMBERS== | ||
| + | *Deficient number is a number <math>n</math> for which the sum of divisors <math>sigma(n)<2n</math>, or, equivalently, the sum of proper divisors (or aliquot sum) <math>s(n)<n</math>. The value <math>2n − sigma(n)</math> (or <math>n − s(n)</math>) is called the number's deficiency. | ||
==Examples== | ==Examples== | ||
Revision as of 01:51, 11 February 2020
PERFECTNUMBERS (Upto,StartFrom)
- is the maximum number limit.
- is the minimum number limit.
is the maximum number limit.
is the minimum number limit.Description
- This function returns the list of Perfect numbers.
- In PERFECTNUMBERS (Upto,StartFrom),Upto is the Maximum number limit to display and Start from is the Minimum number to start Perfect number list.
- Perfect number is a positive integer which is equal to the sum of its proper divisors.
- The smallest perfect number is 6, which is the sum of 1, 2, and 3.
ABUNDANTNUMBERS
- Abundant number is a number for which the sum of its proper divisors is greater than the number itself.
- It is also called Excessive Number.
- The first Abundant number is 12.
- Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16.
- The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4.
- ABUNDANTNUMBERS(110) = 12 18 20 24 30 36 40 42 48 54 56 60 66 70 72 78 80 84 88 90 96 100 102 104 108
DEFICIENTNUMBERS
- Deficient number is a number for which the sum of divisors , or, equivalently, the sum of proper divisors (or aliquot sum) . The value Failed to parse (syntax error): {\displaystyle 2n − sigma(n)} (or Failed to parse (syntax error): {\displaystyle n − s(n)} ) is called the number's deficiency.
for which the sum of divisors 
, or, equivalently, the sum of proper divisors (or aliquot sum) 
. The value Failed to parse (syntax error): {\displaystyle 2n − sigma(n)}
(or Failed to parse (syntax error): {\displaystyle n − s(n)}
) is called the number's deficiency.Examples
- PERFECTNUMBERS(14,2) = 6
- PERFECTNUMBERS(900,54) = 6 28 496
- PERFECTNUMBERS(-567,0) = NaN
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