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Grassmann number. In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber ), is an element of the exterior algebra over the complex numbers. [1] The special case of a 1-dimensional algebra is known as a dual number. Grassmann numbers saw an early use in physics to express a ...
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 ...
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.
Palindromic number. A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word (such as rotor or ...
Deficient number. In number theory, a deficient number or defective number is a positive integer n for which the sum of divisors of n is less than 2n. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is ...
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 ...
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