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Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3.
64 is: the smallest number with exactly seven divisors, [3] the first whole number (greater than one) that is both a perfect square, and a perfect cube, [4] the lowest positive power of two that is not adjacent to either a Mersenne prime or a Fermat prime, the fourth superperfect number — a number such that σ(σ(n)) = 2n, [5]
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [ 1 ] [ 2 ] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89 .
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
A perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square integer. Entertainment
Perfect and superperfect numbers are examples of the wider class of m-superperfect numbers, which satisfy =, corresponding to m = 1 and 2 respectively. For m ≥ 3 there are no even m-superperfect numbers. [1] The m-superperfect numbers are in turn examples of (m,k)-perfect numbers which satisfy [3]
Toggle Definition and examples subsection. ... 49 64 81 100 π 2 / 6 [3] ... The simplest example of this is the sequence of square triangular numbers.
A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m.Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers.