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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]
64: 49: 48: 33 The order 8 square is interesting in itself since it is an instance of the most-perfect magic square. ... coining the words pandiagonal square and most ...
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.
49 89 489 889 4889 8889 48889 88889 n odd: 5 ... 64 413 + + n even with exactly 3 prime factors 1 3 ... , or else it is a perfect square = , in which case n ...
This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by Leonhard Euler: even numbers are perfect if and only if they can be expressed in the form 2 p−1 × (2 p − 1), where 2 p − 1 is a Mersenne prime. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form.
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 ...
SOURCE: Integrated Postsecondary Education Data System, Eastern Kentucky University (2014, 2013, 2012, 2011, 2010).Read our methodology here.. HuffPost and The Chronicle examined 201 public D-I schools from 2010-2014.
An odd superperfect number n would have to be a square number such that either n or ... perfect numbers are (1,2) ... 64, 4096, 65536, 262144, 1073741824 ...