280 (two hundred ndeighty) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

after 279 and before 281.

In mathematics

The denominator of the eighth

harmonic number In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \do ...

, 280 is an octagonal number. 280 is the smallest octagonal number that is a half of another octagonal number. There are 280 plane

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

s with ten nodes. As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations).

In geography

List of highways numbered 280 Route 280, or Highway 280, may refer to: Australia * McIvor Highway Canada * Manitoba Provincial Road 280 * New Brunswick Route 280 Japan * Japan National Route 280 United States * Interstate 280 (disambiguation), Interstate 280 (multiple high ...

Integers from 281 to 289

281

282

282 = 2·3·47,

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

, number of planar partitions of 9

283

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...

with 281, strictly non-palindromic number, 4²⁸³ - 3²⁸³ is prime

284

284 and

220 __NOTOC__ Year 220 ( CCXX) was a leap year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Antonius and Eutychianus (or, less frequently, year 973 '' ...

form the first pair of

amicable number Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, σ(''a'')=''b'' and σ(''b'')=''a'', where σ(''n'') is equal to the sum of positive d ...

s, as the divisors of 284 add up to 220 and vice versa.

285

285 = 3·5·19,

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a bro ...

, Harshad number,

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Example ...

in base 7 (555), vertically symmetric number , also in ''

Star Trek ''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vari ...

'', the total number of

Rules of Acquisition In the fictional ''Star Trek'' universe, the Rules of Acquisition are a collection of sacred business proverbs of the ultra-capitalist race known as the Ferengi. The first mention of rules in the ''Star Trek'' universe was in " The Nagus", an e ...

286

286 = 2·11·13,

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is, ...

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...

, also shorthand for the

Intel 80286 The Intel 80286 (also marketed as the iAPX 286 and often called Intel 286) is a 16-bit microprocessor that was introduced on February 1, 1982. It was the first 8086-based CPU with separate, non- multiplexed address and data buses and also the ...

microprocessor chip. 286 is the smallest even

pseudoprime A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime. Pseudoprimes are classified according to which property of primes they satisfy. Some sources use the term pseudoprime to ...

(not divisible by 3) to base 3, which implies 3²⁸⁵ ≡ 1 (mod 286).

287

287 = 7·41, sum of three consecutive primes (89 + 97 + 101), sum of five consecutive primes (47 + 53 + 59 + 61 + 67), sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47),

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

, also shorthand for the Intel math coprocessor to the 80286

288

289

289 = 17²,

centered octagonal number A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the od ...

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, pa ...

since (8 + 9)² = 289.

References

{{DEFAULTSORT:280 (Number) Integers