Arithmetic dynamics

pair of integers related by their divisors

natural number

number for which the sum of its proper divisors is greater than the number itself

conjecture in mathematics that concerns sequences

natural integer number for which the sum of its proper strict divisors (other than itself) is less than the number itself

numbers with a certain property involving recursive summation

non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again

numbers whose aliquot sums form a cyclic sequence

hypothetical number whose sum of divisors is twice the number plus 1

natural number

integer expressible as the sum of the (number of digits)th power of each of its digits

positive integer unexpressable as the sum of all proper divisors of any other integer

sum of a number's digits

number

natural number whose proper divisors sum to one less than itself

integer that appears as a term in a linear recurrence relation with initial terms based on its own digits

mathematical recursive sequence

a natural number whose square "ends" in the same digits as the number itself

a natural number that cannot be written as the sum of any other natural number n and the individual digits of n

repeated digital sum

number whose divisors add to a multiple of that number

sum of all proper divisors of a natural number

pairs of positive integers such that the sum of the proper divisors of either number is one more than the other number

perfect cube whose cube root is equal to the sum of the original number's digits

In number theory, a factorion in a given number base b 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.

integer equal to the sum of each digit in the number raised to itself

positional numeral system with signed digits; the representation may not be unique

sequence hypothesized to always terminate at 1