145 (number) explained

Number:	145
Divisor:	1, 5, 29, 145

145 (one hundred [and] forty-five) is the natural number following 144 and preceding 146.

In mathematics

• Although composite, 145 is a Fermat pseudoprime in sixteen bases with b < 145. In four of those bases, it is a strong pseudoprime: 1, 12, 17, and 144.
• the Mertens function returns 0.^[1]
• 145 is a pentagonal number^[2] and a centered square number.^[3]

145 = 12 ^{2} + 1 ^{2} = 8 ^{2} + 9 ^{2} . 145 is the fourth number that is the sum of two different pairs of squares. Also, 145 is the result of 3⁴ + 4³, making it a Leyland number.145 = 1 ! + 4 ! + 5 ! , making it a factorion.^[4] The only other numbers that have this property 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 square number and a factorial in 3 ways. The next number with this property is 46249.^[5]

In the military

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

In sports

• The Grand Union Canal Race is a 145-mile ultramarathon from Birmingham to London along the Grand Union Canal

In transportation

• Eurocopter EC 145 is a twin-engine light utility helicopter
• The Delahaye 145 Sports Car from 1938^[6]
• The Alfa Romeo 145 car produced between 1994 and 2001
• Volvo 145 Express station wagon
• ERJ 145 regional jets produced by Embraer
• Golden Gate Transit Bus Route 145^[7]
• London Bus Route 145^[8]

In other fields

145 is also:

• The year AD 145 or 145 BC
• 145 AH is a year in the Islamic calendar that corresponds to 762 – 763 CE
• 145 Adeona is a large main belt asteroid
• Psalm 145
• Sonnet 145
• Apple Computer laptops, such as the PowerBook 145 and PowerBook 145B
• Puff Daddy song “Picture it” includes the lyrics “in something foreign soarin’ 145”
• Tsuu T'ina Nation 145 Indian reserve in Alberta, Canada
• 145 mg medicine tablets, as with Tricor
• "One Four Five" is a song by The Cat Empire

See also

• List of highways numbered 145
• United Nations Security Council Resolution 145
• United States Supreme Court cases, Volume 145

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140

External links

• The Natural Number 145
• Web site: Parker. Matt. 145 and the Melancoil. Numberphile. Brady Haran. 2013-04-06. https://web.archive.org/web/20130514215714/http://www.numberphile.com/videos/melancoil.html. 2013-05-14. dead.

Notes and References

1. Web site: Sloane's A028442 : Numbers n such that Mertens' function is zero. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-28.
2. Web site: Sloane's A000326 : Pentagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-28.
3. Web site: Sloane's A001844 : Centered square numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-28.
4. Web site: Sloane's A014080 : Factorions. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-28.
5. Web site: A359013 - OEIS . 2022-12-11 . The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Web site: 1938 Delahaye 145 le mans Slot Car 1/32 . www.tertrerouge-racingcars.com . 14 January 2022 . https://web.archive.org/web/20080916185903/http://www.tertrerouge-racingcars.com/Delahaye145sports.html . 16 September 2008 . dead.
7. Web site: Ferry Schedules & Maps - Ferry | Golden Gate.
8. Web site: Route 145. London Bus Routes.