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220 (number)

Natural number

Natural number

FieldValue
number220
divisor1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

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. Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number.

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) both of the primes must be greater than or equal to 23. There are exactly 220 different ways of partitioning 64 = 82 into a sum of square numbers.

It is a tetrahedral number, the sum of the first ten triangular numbers, 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.

Notes

References

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

References

  1. Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 167
  2. Higgins, Peter. (2008). "Number Story: From Counting to Cryptography". Copernicus.
  3. {{Cite OEIS. A005153. Practical numbers
  4. {{Cite OEIS. A034963. Sums of four consecutive primes
  5. {{Cite OEIS. A025018. Numbers n such that least prime in Goldbach partition of n increases
  6. {{Cite OEIS. A037444. Number of partitions of n^2 into squares
  7. {{Cite OEIS. A000292. Tetrahedral (or triangular pyramidal) numbers
  8. {{Cite OEIS. A006566. Dodecahedral numbers
  9. {{Cite OEIS. A007678. Number of regions in regular n-gon with all diagonals drawn
  10. {{Cite OEIS. A024916
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