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 n ...
after
279
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Year 279 ( CCLXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Paternus (or, less frequently, year 1032 ...
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, \dot ...
, 280 is an
octagonal number
An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are
: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341 ...
. 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 (multiple highways)
* U.S. Route 280
* Arizo ...
See also the year
280
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Year 280 ( CCLXXX) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Messalla and Gratus (or, less frequently, year 1033 '' ...
.
Integers from 281 to 289
281
282
282 = 2·3·47,
sphenic number, number of planar partitions of 9
283
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 pr ...
with 281, strictly non-palindromic number,
4283 - 3283 is prime
284
284 and
220
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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 numbers, as the divisors of 284 add up to 220 and vice versa.
285
285 = 3·5·19,
sphenic number,
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 broa ...
, Harshad number,
repdigit 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", a ...
.
286
286 = 2·11·13,
sphenic number,
tetrahedral number,
nontotient, also shorthand for the
Intel 80286 microprocessor chip.
286 is the smallest even
pseudoprime (not divisible by 3) to base 3, which implies 3
285 ≡ 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, also shorthand for the Intel math coprocessor to the 80286
288
289
289 = 17
2,
centered octagonal number,
Friedman number since (8 + 9)
2 = 289.
References
{{DEFAULTSORT:280 (Number)
Integers