145 (one hundred ndforty-five) 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 ...

following

144 144 may refer to: * 144 (number), the natural number following 143 and preceding 145 * AD 144, a year of the Julian calendar, in the second century AD * 144 BC, a year of the pre-Julian Roman calendar * 144 (film), ''144'' (film), a 2015 Indian com ...

and preceding 146.

In mathematics

* Although composite, 145 is a

Fermat pseudoprime In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Definition Fermat's little theorem states that if ''p'' is prime and ''a'' is coprime to ''p'', then ''a'p''� ...

to sixteen bases with b < 145. In four of those bases, it is a

strong pseudoprime A strong pseudoprime is a composite number that passes the Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites also pass, making them "pseudoprimes". Unlike the Fermat pseudoprimes, for which there ex ...

: 1, 12, 17, and 144. * Given 145, the

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...

returns 0. * 145 is a

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 ...

and a

centered square number In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...

. *

145 = 12^2 + 1^2 = 8^2 + 9^2

. 145 is the fourth number that is the sum of two different pairs of

squares In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

. Also, 145 is the result of 3⁴ + 4³, making it a

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, ...

. *

145 = 1! + 4! + 5!

, making it a

factorion In number theory, a factorion in a given number base b is a natural number that equals the sum of the factorials of its digits. The name factorion was coined by the author Clifford A. Pickover. Definition Let n be a natural number. For a base b > ...

. The only other numbers that have the property that they are the sum of the

factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \t ...

s of their digits are 1, 2 and 40585. *

145=5^2+5!=11^2+4!=12^2+1!

, making 145 the smallest number that can be written as the sum of a perfect square and a factorial in more than 2 distinct ways. The next number with this property is 46249.

In the military

* was a

United States Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage ...

during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy following World War II

In sports

* The

Grand Union Canal Race The Grand Union Canal Race (GUCR) is an ultramarathon run from the centre of Birmingham to the centre of London along the Grand Union Canal The Grand Union Canal in England is part of the British canal system. It is the principal navigabl ...

is a 145-mile

ultramarathon An ultramarathon, also called ultra distance or ultra running, is any footrace longer than the traditional marathon length of . Various distances are raced competitively, from the shortest common ultramarathon of to over . 50k and 100k are bot ...

from

Birmingham Birmingham ( ) is a city and metropolitan borough in the metropolitan county of West Midlands in England. It is the second-largest city in the United Kingdom with a population of 1.145 million in the city proper, 2.92 million in the West ...

to London along the

Grand Union Canal The Grand Union Canal in England is part of the British canal system. It is the principal navigable waterway between London and the Midlands. Starting in London, one arm runs to Leicester and another ends in Birmingham, with the latter st ...

In transportation

Eurocopter EC 145 The Eurocopter EC145 (now Airbus Helicopters H145) is a twin-engine light utility helicopter developed and manufactured by Airbus Helicopters. Originally designated as the ''BK 117'', the H145 is based upon the MBB/Kawasaki BK 117 C1, which ...

is a twin-engine light utility

helicopter A helicopter is a type of rotorcraft in which lift and thrust are supplied by horizontally spinning rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and laterally. These attributes ...

The Delahaye 145 Sports Car ''The'' () is a grammatical article in English, denoting persons or things already mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the m ...

from 1938 * The Alfa Romeo 145 car produced between 1994 and 2001 * Volvo 145 Express station wagon * ERJ 145

regional jets A regional jet (RJ) is a jet-powered regional airliner with fewer than 100 seats. The first one was the Sud-Aviation Caravelle in 1959, followed by the widespread Yakovlev Yak-40, Fokker F-28, and BAe 146. The 1990s saw the emergence of th ...

produced by

Embraer Embraer S.A. () is a Brazilian multinational aerospace manufacturer that produces commercial, military, executive and agricultural aircraft, and provides aeronautical services. It was founded in 1969 in São José dos Campos, São Paulo, where i ...

* Golden Gate Transit Bus Route 145 * London Bus Route 145

In other fields

145 is also: * The year AD 145 or 145 BC * 145 AH is a year in the

Islamic calendar The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ, translit=al-taqwīm al-hijrī), also known in English as the Muslim calendar and Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or ...

that corresponds to 762 – 763 CE *

145 Adeona Adeona ( minor planet designation: 145 Adeona) is a large asteroid from the intermediate asteroid belt, approximately in diameter. Its surface is very dark, and, based upon its classification as a C-type asteroid, is probably composed of primit ...

is a large

main belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...

asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

Psalm 145 Psalm 145 is the 145th psalm of the Book of Psalms, generally known in English by its first verse, in the King James Version, "I will extol thee, my God, O king; and I will bless thy name for ever and ever". In Latin, it is known as "Exaltabo ...

Sonnet 145 Sonnet 145 is one of Shakespeare's sonnets. It forms part of the Dark Lady sequence of sonnets and is the only one written not in iambic pentameter, but instead tetrameter. It is also the Shakespeare sonnet which uses the fewest letters. It is ...

Apple Computer Apple Inc. is an American multinational technology company headquartered in Cupertino, California, United States. Apple is the largest technology company by revenue (totaling in 2021) and, as of June 2022, is the world's biggest company b ...

laptops, such as the

PowerBook 145 The PowerBook 140 was released in the first line of PowerBooks. It was the mid-range PowerBook, between the low-end 100 and the high-end 170. As with the PowerBook 170, and unlike the 100, this PowerBook featured an internal floppy drive. Coden ...

and

PowerBook 145B The PowerBook 140 was released in the first line of PowerBooks. It was the mid-range PowerBook, between the low-end 100 and the high-end 170. As with the PowerBook 170, and unlike the 100, this PowerBook featured an internal floppy drive. Codena ...

Puff Daddy Puff may refer to: Science and technology * Puff, a small quantity of gas or smoke in the air ** Puff, a light gust of wind ** Exhalation ** Inhalation * Puff model, volcanic ash tracking model developed at the University of Alaska Fairbanks * PUF ...

song “Picture it” includes the lyrics “in something foreign soarin’ 145” * Tsuu T'ina Nation 145

Indian reserve In Canada, an Indian reserve (french: réserve indienne) is specified by the '' Indian Act'' as a "tract of land, the legal title to which is vested in Her Majesty, that has been set apart by Her Majesty for the use and benefit of a band." Ind ...

Alberta Alberta ( ) is one of the thirteen provinces and territories of Canada. It is part of Western Canada and is one of the three prairie provinces. Alberta is bordered by British Columbia to the west, Saskatchewan to the east, the Northwest Ter ...

, Canada * 145 mg medicine tablets, as with

Tricor Fenofibrate (sold under the brand names ''Tricor'', ''Fenobrat'' etc.), is an oral medication of the fibrate class used to treat abnormal blood lipid levels. It is less commonly used compared than statins because it treats a different type of ...

* "One Four Five" is a song by

The Cat Empire The Cat Empire are an Australian jazz/funk band, formed in Melbourne, Victoria, in 1999. For most of the band's duration, the core members were Felix Riebl (lead vocals, percussion), Harry James Angus (trumpet, vocals), Will Hull-Brown (drums), ...

References

* Wells, D. ''

The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, ...

'' London: Penguin Group. (1987): 140

External links

The Natural Number 145
* {{DEFAULTSORT:145 (Number) Integers