Multiplicative digital root
In number theory, the multiplicative digital root of a natural number in a given number base is found by multiplying the digits of together, then repeating this operation until only a single-digit rem
Automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base whose square "ends" in the same digits as the number itself.
Kaprekar's routine
In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by
Sociable number
In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of amicable numbers and perfect numbers. The first two sociable seque
6174 (number)
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: 1.
* Take any four-digit number, using at least two different digit
Self number
In number theory, a self number or Devlali number in a given number base is a natural number that cannot be written as the sum of any other natural number and the individual digits of . 20 is a self n
Untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are
Hyperperfect number
In mathematics, a k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n) − n − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n). A
Dudeney number
In number theory, a Dudeney number in a given number base is a natural number equal to the perfect cube of another natural number such that the digit sum of the first natural number is equal to the se
Factorion
In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. The name factorion was coined by the author Clifford A. Pickover.
Sum-product number
A sum-product number in a given number base is a natural number that is equal to the product of the sum of its digits and the product of its digits. There are a finite number of sum-product numbers in
Collatz conjecture
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integ
Aliquot sum
In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself.That is, It can be used to characterize the prime
Signed-digit representation
In mathematical notation for numbers, a signed-digit representation is a positional numeral system with a set of signed digits used to encode the integers. Signed-digit representation can be used to a
Juggler sequence
In number theory, a juggler sequence is an integer sequence that starts with a positive integer a0, with each subsequent term in the sequence defined by the recurrence relation:
Digit sum
In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number would be .
Aliquot sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since t
Arithmetic dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the c
Abundant number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper diviso
Betrothed numbers
Betrothed numbers or quasi-amicable numbers are two positive integers such that the sum of the proper divisors of either number is one more than the value of the other number. In other words, (m, n) a
Keith number
In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number in a given number base with digits such that when a sequence is created such that th
Happy number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because , and . On the other hand, 4 is
Meertens number
In number theory and mathematical logic, a Meertens number in a given number base is a natural number that is its own Gödel number. It was named after Lambert Meertens by Richard S. Bird as a present
Perfect digital invariant
In number theory, a perfect digital invariant (PDI) is a number in a given number base that is the sum of its own digits each raised to a given power.
196 (number)
196 (one hundred [and] ninety-six) is the natural number following 195 and preceding 197.
Lychrel number
A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called t
Multiply perfect number
In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is called k-perfect (
Quasiperfect number
In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Equivalently, n is the sum of its non-trivial divisors
Digital root
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result fro
Perfect digit-to-digit invariant
In number theory, a perfect digit-to-digit invariant (PDDI; also known as a Munchausen number) is a natural number in a given number base that is equal to the sum of its digits each raised to the powe
Amicable numbers
Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, σ(a)=b and σ(b)=a, where σ(n) is equal to th
Almost perfect number
In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function
Deficient number
In number theory, a deficient number or defective number is a number 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
Kaprekar number
In mathematics, a natural number in a given number base is a -Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has digits, that add u
Narcissistic number
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus perfect number) in a given number base is a num