220 (number)
| ||||
|---|---|---|---|---|
| Cardinal | two hundred twenty | |||
| Ordinal | 220th (two hundred twentieth) | |||
| Factorization | 22 × 5 × 11 | |||
| Greek numeral | ΣΚ´ | |||
| Roman numeral | 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.
In mathematics
[edit]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
[edit]- ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
- ^ Sloane, N. J. A. (ed.). "Sequence A005153 (Practical numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034963 (Sums of four consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A025018 (Numbers n such that least prime in Goldbach partition of n increases)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A037444 (Number of partitions of n^2 into squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006566 (Dodecahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
References
[edit]- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 145 – 147). London: Penguin Group.