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55 (number)
55 (fifty-five) is the natural number following 54 (number), 54 and preceding 56 (number), 56. Mathematics 55 is: *the 10th Fibonacci number and the 10th triangular number, The sum of 55's digits is also 10. *the 5th heptagonal number, the 5th square pyramidal number, and the 4th centered nonagonal number. 55 is also the 19th semiprime and the 15th squarefree semiprime, as well as the 32nd Nontotient, nontotient number (including odd numbers > 1) the 36th arithmetic number, the 38th composite number (where the Abundant number, abundance of 55 = - 38), the 43rd deficient number, the 45th Polite number#Trapezoidal numbers, trapezoidal number, and the 49th polite number. Transportation *In the United States, the National Maximum Speed Law prohibited speed limits higher than from 1974 to 1987. The number ''55'' became a popular shorthand for the 55 mph speed limit. For example, a hand with a pair of fives in Texas hold'em poker is referred to as a "speed limit". Referenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 nontotient if there is no integer ''x'' that has exactly ''n'' coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions ''x'' = 1 and ''x'' = 2. The first few even nontotients are this sequence: : 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, ... The least value of ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) are this sequence: :1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Maximum Speed Law
The National Maximum Speed Limit (NMSL) was a provision of the federal government of the United States 1974 Emergency Highway Energy Conservation Act that effectively prohibited speed limits higher than . The limit was increased to in 1987. It was drafted in response to oil price spikes and supply disruptions during the 1973 oil crisis. Even after fuel costs began to decrease over time the law would remain in place until 1995 as proponents claimed it reduced traffic fatalities. While federal officials hoped gasoline consumption would fall by 2.2%, the actual savings were estimated at between 0.5% and 1%. The law was widely disregarded by motorists nationwide, and some U.S. state, states opposed the law, but many jurisdictions discovered it to be a major source of revenue. Actions ranged from proposing deals for an exemption to de-emphasizing speed limit enforcement. The NMSL was modified in 1987 and 1988 to allow up to limits on certain limited-access rural roads. Congress ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polite Number
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite... The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two. Polite numbers have also been called staircase numbers because the Young diagrams which represent graphically the partitions of a polite number into consecutive integers (in the French notation of drawing these diagrams) resemble staircases. If all numbers in the sum are strictly greater than one, the numbers so formed are also called trapezoidal numbers because they represent patterns of points arranged in a trapezoid.. The problem of representing numbers as sums of consecutive integers and of counting the number of representations of this type has been studied by Sylvester,. IThe collected mathematical papers of James Joseph Sylvester (December 1904) H. F. Bake ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deficient Number
In number theory, a deficient number or defective number is a positive integer for which the sum of divisors of is less than . Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than . For example, the proper divisors of 8 are , and their sum is less than 8, so 8 is deficient. Denoting by the sum of divisors, the value is called the number's deficiency. In terms of the aliquot sum , the deficiency is . Examples The first few deficient numbers are :1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, ... As an example, consider the number 21. Its divisors are 1, 3, 7 and 21, and their sum is 32. Because 32 is less than 42, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10. Properties Since the aliquot sums of prime numbers equal 1, all prime numbers are deficient. More generally, all odd numbers with one or two distinct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abundant Number
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example. Definition An ''abundant number'' is a natural number for which the Divisor function, sum of divisors satisfies , or, equivalently, the sum of proper divisors (or aliquot sum) satisfies . The ''abundance'' of a natural number is the integer (equivalently, ). Examples The first 28 abundant numbers are: :12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, ... . For example, the proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12, whose sum is 36. Because 36 is greater than 24, the number 24 is abundant. Its abundance is 36 − 24&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime number, prime, or the Unit (ring theory), unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Number
In number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is :\frac=3, which is also an integer. However, 2 is not an arithmetic number because its only divisors are 1 and 2, and their average 3/2 is not an integer. The first numbers in the sequence of arithmetic numbers are :1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, ... . The arithmetic means of the divisors of arithmetic numbers are listed at . Density It is known that the natural density of such numbers is 1:Guy (2004) p.76 indeed, the proportion of numbers less than ''X'' which are not arithmetic is asymptotically :\exp\left( \,\right) where ''c'' = 2 + o(1). A number ''N'' is arithmetic if the number of divisors ''d''(''N'') divides the sum of divisors σ(''N''). It is known that the density De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
54 (number)
54 (fifty-four) is the natural number and Sign (math), positive integer following 53 (number), 53 and preceding 55 (number), 55. As a multiple of 2 but not of 4, 54 is an Singly and doubly even, oddly even number and a composite number. 54 is related to the golden ratio through trigonometry: the sine of a 54 degree angle is half of the golden ratio. Also, 54 is a regular number, and its even division of powers of 60 was useful to ancient mathematicians who used the Assyro-Babylonian mathematics system. It is also an abundant number, since Aliquot sum, the sum of its proper divisors (66) is greater than itself. In mathematics Number theory 54 is an abundant number because Aliquot sum, the sum of its proper divisors (66 (number), 66), which excludes 54 as a divisor, is greater than itself. Like all multiples of 6, 54 is equal to some of its proper divisors summed together, so it is also a semiperfect number. These proper divisors can be summed in various ways to express all posit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Nonagonal Number
A centered nonagonal number, (or centered enneagonal number), is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for ''n'' layers is given by the formula :Nc(n) = \frac. Multiplying the (''n'' - 1)th triangular number by 9 and then adding 1 yields the ''n''th centered nonagonal number, but centered nonagonal numbers have an even simpler relation to triangular numbers: every third triangular number (the 1st, 4th, 7th, etc.) is also a centered nonagonal number. Thus, the first few centered nonagonal numbers are : 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946. The list above includes the perfect numbers 28 and 496. All even perfect numbers are triangular numbers whose index is an odd Mersenne prime. Since every Mersenne prime greater than 3 is congruent to 1 modulo In computing and mathematics, the modulo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
