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A positive integer that can be written as the sum of two or more consecutive positive integers. A138591: Erdős–Nicolas numbers: 24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ... A number n such that there exists another number m and , =. A194472: Solution to Stepping Stone Puzzle
The transitivity of M implies that the integers and integer sequences inside M are actually integers and sequences of integers. An integer sequence is a definable sequence relative to M if there exists some formula P ( x ) in the language of set theory, with one free variable and no parameters, which is true in M for that integer sequence and ...
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form (+). [1] The study of these numbers dates back to Aristotle.They are also called oblong numbers, heteromecic numbers, [2] or rectangular numbers; [3] however, the term "rectangular number" has also been applied to the composite numbers.
Composite numbers have also been called "rectangular numbers", but that name can also refer to the pronic numbers, numbers that are the product of two consecutive integers. Yet another way to classify composite numbers is to determine whether all prime factors are either all below or all above some fixed (prime) 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 . [ 1 ] [ 2 ] The impolite numbers are exactly the powers of two , and the polite numbers are the natural numbers that are not powers of two.
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member. [ 5 ] The only known number n such that φ( n − 1)σ( n − 1) = φ( n )σ( n ) = φ( n + 1)σ( n + 1) , where φ( m ) is Euler's totient function and σ( n ) is the ...
Number of consecutive integers starting with n needed to sum to a Niven number. Jul 8, 2005: A112886: Triangle-free positive integers. Jan 12, 2006: A120007: Möbius transform of sum of prime factors of n with multiplicity. Jun 2, 2006