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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
In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 1 1 + 3 2 + 0 3 + 6 4. 135, 175, 518, and 598 also have this property. Centered triangular number. [125] 1307 = safe prime [22] 1308 = sum of totient function for first 65 integers; 1309 = the first sphenic number followed by two consecutive such number
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
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...
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.
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 ...
Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. [11] The sum of the integers from 1 to 36 is 666 (see number of the beast). 36 is also a Tridecagonal number. [12]
an Erdős–Woods number, since it is possible to find sequences of 88 consecutive integers such that each inner member shares a factor with either the first or the last member. [5] a palindromic number in bases 5 (323 5), 10 (88 10), 21 (44 21), and 43 (22 43). a repdigit in bases 10, 21 and 43. a 2-automorphic number. [6]