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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 one million, there are 24 ...
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as madam or racecar, the date "22/02/2022" and the sentence: "A man, a plan, a canal – Panama ". The 19-letter Finnish word saippuakivikauppias (a soapstone vendor), is the longest single-word palindrome in everyday use, while ...
An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k.
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 ...
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 ...
[f] 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). [15] However, in the definition of perfect number which comes shortly afterward, Euclid treats 1 as a number like any ...
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 32 and can be written as 3 × 3 . The usual notation for the square of a number n is not the product n × n, but the equivalent ...
An abundant number which is not the multiple of an abundant number or perfect number (i.e. all its proper divisors are deficient) is called a primitive abundant number An abundant number whose abundance is greater than any lower number is called a highly abundant number, and one whose relative abundance (i.e. s(n)/n ) is greater than any lower ...