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245 (number)
245 (two hundred ndforty-five) is the natural number following 244 and preceding 246. Additionally, 245 is: *a composite number. *a stella octangula number. *palindromic in bases 34 (7734) and 48 (5548) *a Harshad number In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ... in bases 7, 9, 11, 15, 31, 35, 36 (and 14 other bases). *the aliquot sum of any of these numbers: 723, 1195, 2563, 3859, *part of the 97-aliquot tree. 4624, 4893, 2595, 1581, 723, 245, References Integers {{Num-stub ... [...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] |
244 (number)
244 (two hundred ndforty-four) is the 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 in ... following 243 and preceding 245. Additionally, 244 is: *the sum of two nonzero fifth powers (). *palindromic in bases 3 (1000013), 11 (20211), 60 (4460), 121 (22121), 243 (11243). *a Harshad number in bases 3, 9, 11, 61, 62, 81, 121, 122, 123 and 184. *the second anti-perfect number, meaning that reversing the digits of the proper divisors of 244 and adding the results gives 244 back again. *part of the sequence 1, 2, 4, 8, 61, 221, 244, ... in which each number is formed by reversing the digits of the double of the previous number. *the number of non-isomorphic set-systems of weight 8 References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
246 (number)
246 (two hundred ndforty-six) is the natural number following 245 and preceding 247. Additionally, 246 is: *an untouchable number. *palindromic in bases 5 (14415), 9 (3039), 40 (6640), 81 (3381), 122 (22122) and 245 (11245). *a Harshad number in bases 2, 3, 6, 7, 9, 11 (and 15 other bases). *the smallest number N for which it is known that there is an infinite number of prime gaps no larger than N. Also: *The aliquot sequence starting at 246 is: 246, 258, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 0. *There are exactly 246 different rooted plane trees with eight nodes, and 246 different necklaces A necklace is an article of jewellery that is worn around the neck. Necklaces may have been one of the earliest types of adornment worn by humans. They often serve Ceremony, ceremonial, Religion, religious, magic (illusion), magical, or Funerar ... with seven black and seven white beads. References Integers {{Num-stub ... [...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] |
Stella Octangula Number
In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form .. The sequence of stella octangula numbers is :0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, ... Only two of these numbers are square. Ljunggren's equation There are only two positive square stella octangula numbers, and , corresponding to and respectively. The elliptic curve describing the square stella octangula numbers, :m^2 = n (2n^2 - 1) may be placed in the equivalent Weierstrass form :x^2 = y^3 - 2y by the change of variables , . Because the two factors and of the square number are relatively prime, they must each be squares themselves, and the second change of variables X=m/\sqrt and Y=\sqrt leads to Ljunggren's equation :X^2 = 2Y^4 - 1 A theorem of Siegel states that every elliptic curve has only finitely many integer solutions, and found a difficult proof that the only integer solutions to his equation were and , corresponding to the two square stel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harshad Number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Because being a Harshad number is determined based on the base the number is expressed in, a number can be a Harshad number many times over. So-called Trans-Harshad numbers are Harshad numbers in every base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. Definition Stated mathematically, let be a positive integer with digits when written in base , and let the digits be a_i (i = 0, 1, \ldots, m-1). (It follows that a_i must be either zero or a positive integer up to .) can be expressed as :X=\sum_^ a_i n^i. is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
