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1980 (number)
1980 is the natural number following 1979 and preceding 1981. Mathematics 1980 is a pronic number, a highly abundant number, an e-perfect number and a coreful perfect number. Not only is it highly abundant, but it also has a greater aliquot sum than any smaller number. 1980 is the fourth number with 36 divisors. It forms an amicable triple with 2016 2016 was designated as: * International Year of Pulses by the sixty-eighth session of the United Nations General Assembly. * International Year of Global Understanding (IYGU) by the International Council for Science (ICSU), the Internationa ... and 2556, since σ(1980) = σ(2016) = σ(2556) and 6552 = 1980 + 2016 + 2556. References Integers {{number-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highly Abundant Number
In number theory, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum of the divisors of any smaller natural number. Highly abundant numbers and several similar classes of numbers were first introduced by , and early work on the subject was done by . Alaoglu and Erdős tabulated all highly abundant numbers up to 104, and showed that the number of highly abundant numbers less than any is at least proportional to . Formal definition and examples Formally, a natural number ''n'' is called highly abundant if and only if for all natural numbers ''m'' < ''n'', :\sigma(n) > \sigma(m) where σ denotes the sum-of-divisors function. The first few highly abundant numbers are : 1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, ... . For instance, 5 is not highly abundant because σ(5) = 5+1 = 6 is smaller than σ(4) = 4 + 2 + 1 = 7, while 8 is highly abundant because σ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number. Examples For example, the proper divisors of 12 (that is, the positive divisors of 12 that are not equal to 12) are , and 6, so the aliquot sum of 12 is 16 i.e. (). The values of for are: :0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 36, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 55, 1, 22, 17, 50, 1, 54, 1, 40, 33, 26, 1, 76, 8, 43, ... Characterization of classes of numbers The aliquot sum function can be used to characterize several notable classes of numbers: *1 is the only number whose aliquot sum is 0. *A number is prime if and only if its aliquot sum is 1. *The aliquot sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a '' multiple'' of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer n is divisible by a nonzero integer m if there exists an integer k such that n=km. This is written as : m\mid n. This may be read as that m divides n, m is a divisor of n, m is a factor of n, or n is a multiple of m. If m does not divide n, then the notation is m\not\mid n. There are two conventions, distinguished by whether m is permitted to be zero: * With the convention without an additional constraint on m, m \mid 0 for every integer m. * With the convention that m be nonzero, m \mid 0 for every nonzero integer m. General Divisors can be negative as well as positive, although often the term is restricted to posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amicable Triple
In mathematics, an amicable triple is a set of three different numbers so related that the ''restricted'' sum of the divisors of each is equal to the sum of other two numbers. In another equivalent characterization, an amicable triple is a set of three different numbers so related that the sum of the divisors of each is equal to the sum of the three numbers. So a triple (''a'', ''b'', ''c'') of natural numbers is called amicable if ''s''(''a'') = ''b'' + ''c'', ''s''(''b'') = ''a'' + ''c'' and ''s''(''c'') = ''a'' + ''b'', or equivalently if σ(''a'') = σ(''b'') = σ(''c'') = ''a'' + ''b'' + ''c''. Here σ(''n'') is the sum of all positive divisors, and ''s''(''n'') = σ(''n'') − ''n'' is the aliquot sum In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characteriz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2016 (number)
2016 is the natural number following 2015 and preceding 2017. Mathematics 2016 is the second-smallest Erdős–Nicolas number after 24. 2016 is a triangular number. 2016 has a total of 36 divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a '' multiple'' of m. An integer n is divisible or evenly divisibl ...s. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
