145 (number)

← 144 145 146 →
← 140 141 142 143 144 145 146 147 148 149 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred forty-five
Ordinal	145th (one hundred forty-fifth)
Factorization	5 × 29
Divisors	1, 5, 29, 145
Greek numeral	ΡΜΕ´
Roman numeral	CXLV, cxlv
Binary	100100012
Ternary	121013
Senary	4016
Octal	2218
Duodecimal	10112
Hexadecimal	9116

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]
• ${\displaystyle 145=12^{2}+1^{2}=8^{2}+9^{2}}$. 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.
• ${\displaystyle 145=1!+4!+5!}$, making it a factorion. ^[4] The only other numbers that have this property are 1, 2 and 40585. ^[4]
• ${\displaystyle 145=5^{2}+5!=11^{2}+4!=12^{2}+1!}$, 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]

References

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

1. "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
3. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
4. "Sloane's A014080 : Factorions". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
5. "A359013 - OEIS". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-11.

External links

• The Natural Number 145
• Parker, Matt. "145 and the Melancoil". Numberphile. Brady Haran. Archived from the original on 2013-05-14. Retrieved 2013-04-06.