220 (number)

Template:Short description Template:Infobox number 220 (two hundred [and] twenty) is the natural number following 219 and preceding 221.

In mathematics

It is a 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.<ref>Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167</ref><ref>Template:Cite book</ref> Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number.<ref>Template:Cite OEIS</ref>

It is the sum of four consecutive primes (47 + 53 + 59 + 61).<ref>Template:Cite OEIS</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>Template:Cite OEIS</ref> There are exactly 220 different ways of partitioning 64 = 8² into a sum of square numbers.<ref>Template:Cite OEIS</ref>

It is a tetrahedral number, the sum of the first ten triangular numbers,<ref>Template:Cite OEIS</ref> and a dodecahedral number.<ref>Template:Cite OEIS</ref> If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions.<ref>Template:Cite OEIS</ref>

It is the sum of the sums of the divisors of the first 16 positive integers.<ref>Template:Cite OEIS</ref>

Notes

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References

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 145 – 147). London: Penguin Group.