View source for 220 (number)

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'''220''' ('''two hundred [and] twenty''') is the [[Natural number|natural number]] following [[219 (number)|219]] and preceding [[221 (number)|221]].

==In mathematics==
It is a [[Composite number|composite number]], with its proper divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with [[284 (number)|284]].<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 167</ref><ref>{{cite book |title=Number Story: From Counting to Cryptography |url=https://archive.org/details/numberstoryfromc00higg_612 |url-access=limited |last=Higgins |first=Peter |year=2008 |publisher=Copernicus |location=New York |isbn=978-1-84800-000-1 |page=[https://archive.org/details/numberstoryfromc00higg_612/page/n69 61] }}</ref> Every number up to 220 may be expressed as a sum of its divisors, making 220 a [[Practical number|practical number]].<ref>{{Cite OEIS|sequencenumber=A005153 |name=Practical numbers}}</ref>

It is the sum of four consecutive primes (47 + 53 + 59 + 61).<ref>{{Cite OEIS|sequencenumber=A034963 |name=Sums of four consecutive primes}}</ref> It is the smallest even number with the property that when represented as a sum of two prime numbers (per [[Goldbach's conjecture]]) both of the primes must be greater than or equal to 23.<ref>{{Cite OEIS|sequencenumber=A025018 |name=Numbers n such that least prime in Goldbach partition of n increases}}</ref>
There are exactly 220 different ways of [[Partition (number theory)|partitioning]] 64&nbsp;=&nbsp;8<sup>2</sup> into a sum of [[Square number|square number]]s.<ref>{{Cite OEIS|sequencenumber=A037444 |name=Number of partitions of n^2 into squares}}</ref>

It is a tetrahedral number, the sum of the first ten [[Triangular number|triangular number]]s,<ref>{{Cite OEIS|sequencenumber=A000292 |name=Tetrahedral (or triangular pyramidal) numbers}}</ref> and a dodecahedral number.<ref>{{Cite OEIS|sequencenumber=A006566 |name=Dodecahedral numbers}}</ref> If all of the diagonals of a regular [[Decagon|decagon]] are drawn, the resulting figure will have exactly 220 regions.<ref>{{Cite OEIS|sequencenumber=A007678 |name=Number of regions in regular n-gon with all diagonals drawn}}</ref>

It is the sum of the sums of the divisors of the first 16 positive integers.<ref>{{Cite OEIS|A024916|name=sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n}}</ref>

==Integers between 221 and 229==

=== 221 ===

{{Main|221 (number)}}

=== 222 ===

{{Main|222 (number)}}

=== 223 ===

{{Main|223 (number)}}

=== 224 ===

{{Main|224 (number)}}

=== 225 ===

{{Main|225 (number)}}

=== 226 ===

{{Main|226 (number)}}

=== 227 ===

{{Main|227 (number)}}

=== 228 ===

{{Main|228 (number)}}

=== 229 ===

{{Main|229 (number)}}

==Notes==
<references/>

==References==
* Wells, D. (1987). ''The Penguin Dictionary of Curious and Interesting Numbers'' (pp.&nbsp;145 – 147). London: Penguin Group.


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[[Category:Integers]]

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