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The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter. The sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17) a tetranacci number [2] and as a multiple of 7 and 8, a pronic number. [3] Interestingly it is one of a few pronic numbers whose digits in decimal also are successive (5 and 6).
In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, = |,. It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.
In number theory, a deficient number or defective number is a positive integer n for which the sum of divisors of n is less than 2n. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is deficient.
Abundancy may also be expressed as () where denotes a divisor function with () equal to the sum of the k-th powers of the divisors of n. The numbers 1 through 5 are all solitary. The smallest friendly number is 6, forming for example, the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14 ...
The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.
The infinity symbol ∞, described as a "sideways figure eight", is unrelated to the digit 8 in origin; it is first used (in the mathematical meaning "infinity") in the 17th century, and it may be derived from the Roman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter, ω.
Song of Songs 8 (abbreviated [where?] as Song 8) is the eighth (and the final) chapter of the Song of Songs in the Hebrew Bible or the Old Testament of the Christian Bible. [1] [2] This book is one of the Five Megillot, a collection of short books, together with Ruth, Lamentations, Ecclesiastes and Esther, within the Ketuvim, the third and the last part of the Hebrew Bible. [3]