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Primitive weird numbers. A property of weird numbers is that if n is weird, and p is a prime greater than the sum of divisors σ(n), then pn is also weird. This leads to the definition of primitive weird numbers: weird numbers that are not a multiple of other weird numbers (sequence A002975 in the OEIS). Among the 1765 weird numbers less than ...
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. [1] For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers ...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
The odious numbers give the positions of the nonzero values in the Thue–Morse sequence. Every power of two is odious, because its binary expansion has only one nonzero bit. Except for 3, every Mersenne prime is odious, because its binary expansion consists of an odd prime number of consecutive nonzero bits. Non-negative integers that are not ...
Oppositional defiant disorder. Oppositional defiant disorder ( ODD) [1] is listed in the DSM-5 under Disruptive, impulse-control, and conduct disorders and defined as "a pattern of angry/irritable mood, argumentative/defiant behavior, or vindictiveness". [2] This behavior is usually targeted toward peers, parents, teachers, and other authority ...
Euclid, for example, defined a unit first and then a number as a multitude of units, thus by his definition, a unit is not a number and there are no unique numbers (e.g., any two units from indefinitely many units is a 2). However, in the definition of perfect number which comes shortly afterward, Euclid treats 1 as a number like any other.
The sum of an even and odd function is not even or odd, unless one of the functions is equal to zero over the given domain. Multiplication and division. The product of two even functions is an even function. That implies that product of any number of even functions is an even function as well. The product of two odd functions is an even function.
In summary, it has been shown that partitions into an even number of distinct parts and an odd number of distinct parts exactly cancel each other, producing null terms 0x n, except if n is a generalized pentagonal number = = /, in which case there is exactly one Ferrers diagram left over, producing a term (−1) k x n. But this is precisely ...