220 (number)

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← 219 220 221 →
Cardinal two hundred twenty
Ordinal 220th
(two hundred twentieth)
Factorization 22 × 5 × 11
Divisors 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
Greek numeral ΣΚ´
Roman numeral CCXX, ccxx
Binary 110111002
Ternary 220113
Senary 10046
Octal 3348
Duodecimal 16412
Hexadecimal DC16

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

Contents

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. [1] [2] Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number. [3]

It is the sum of four consecutive primes (47 + 53 + 59 + 61). [4] 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. [5] There are exactly 220 different ways of partitioning 64 = 82 into a sum of square numbers. [6]

It is a tetrahedral number, the sum of the first ten triangular numbers, [7] and a dodecahedral number. [8] If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions. [9]

It is the sum of the sums of the divisors of the first 16 positive integers. [10]

Notes

  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 . New York: Copernicus. p.  61. ISBN   978-1-84800-000-1.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA005153(Practical numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA034963(Sums of four consecutive primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA025018(Numbers n such that least prime in Goldbach partition of n increases)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA037444(Number of partitions of n^2 into squares)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA000292(Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA006566(Dodecahedral numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. ↑ Sloane, N. J. A. (ed.). "SequenceA007678(Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. ↑ Sloane, N. J. A. (ed.). "SequenceA024916(sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.

References

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