220 (two hundred
ndtwenty) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
following
219
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Year 219 ( CCXIX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Antonius and Sacerdos (or, less frequently, year 972 ''Ab ...
and preceding
221
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Year 221 ( CCXXI) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Gratus and Vitellius (or, less frequently, year 974 ''Ab ...
.
In mathematics
It is a
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor
In mathematics, a divisor of an integer n, also called a factor ...
, with its proper divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an
amicable number with
284. Every number up to 220 may be expressed as a sum of its divisors, making 220 a
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. For example, 12 is a practical number because all the numbers from 1 ...
.
It is the sum of four consecutive primes (47 + 53 + 59 + 61). It is the smallest even number with the property that when represented as a sum of two prime numbers (per
Goldbach's conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
The conjecture has been shown to hold ...
) both of the primes must be greater than or equal to 23.
There are exactly 220 different ways of
partitioning 64 = 8
2 into a sum of
square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The u ...
s.
It is a
tetrahedral number, the sum of the first ten
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
s, and a dodecahedral number. If all of the diagonals of a regular
decagon are drawn, the resulting figure will have exactly 220 regions.
It is the sum of the sums of the divisors of the first 16
positive integers
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
.
Notes
References
* Wells, D. (1987). ''
The Penguin Dictionary of Curious and Interesting Numbers'' (pp. 145 – 147). London: Penguin Group.
{{DEFAULTSORT:220 (Number)
Integers