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The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.
The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. A059756: Sierpinski numbers: 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ... Odd k for which { k⋅2 n + 1 : n ∈ } consists only of composite numbers. A076336
105 is the 14th triangular number, [1] a dodecagonal number, [2] and the first Zeisel number. [3] It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7. [4] It is also the sum of the first five square pyramidal numbers. 105 comes in the middle of the prime quadruplet (101, 103 ...
Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8.
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.
y = x 3 for values of 1 ≤ x ≤ 25.. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
An odd prime p is a generalized Fermat number if and only if p is congruent to 1 (mod 4). (Here we consider only the case n > 0, so 3 = + is not a counterexample.) An example of a probable prime of this form is 200 262144 + 119 262144 (found by Kellen Shenton). [16]