Search results
Results from the WOW.Com Content Network
Quasi-sociable numbers or reduced sociable numbers are numbers whose aliquot sums minus one form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of betrothed numbers and quasiperfect numbers. The first quasi-sociable sequences, or quasi-sociable chains, were discovered by Mitchell Dickerman ...
In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion. [1] These numbers give the positions of the zero values in the Thue–Morse sequence, and for this reason they have also been called the Thue–Morse set. [2] Non-negative integers that are not evil are called odious numbers.
In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal.Like the related Fibonacci numbers, they are a specific type of Lucas sequence (,) for which P = 1, and Q = −2 [1] —and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number ...
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, s ( a )= b and s ( b )= a , where s ( n )=σ( n )- n is equal to the sum of positive divisors of n except n itself (see also divisor function ).
The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of ...
The Erdős–Woods numbers can be characterized in terms of certain partitions of the prime numbers.A number k is an Erdős–Woods number if and only if the prime numbers less than k can be partitioned into two subsets X and Y with the following property: for every pair of positive integers x and y with x + y = k, either x is divisible by a prime in X, or y is divisible by a prime in Y.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
The Fortunate number for p n # is always above p n and all its divisors are larger than p n. This is because p n #, and thus p n # + m, is divisible by the prime factors of m not larger than p n. If a composite Fortunate number does exist, it must be greater than or equal to p n+1 2. [citation needed] The Fortunate numbers for the first ...