integer-valued function
function that ranges over the integers
arithmetic derivative
function defined on integers in number theory
integer part
part to the left of the decimal separator of a number
permutation
change of ordering in a (mathematical) set
rank
measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by a matrix
divisor sum function
the arithmetic function mapping a positive integer to the sum of all its positive divisors (including itself)
parity of a permutation
group homomorphism from the symmetric group over a finite set to the two-element group {±1}
number of divisors
number of different natural numbers that evenly divide the given number
Kronecker delta
function
floor and ceiling functions
functions of a real returning respectively the largest smaller and the smallest larger integer
Landau's function
function which returns the largest least common multiple of any partition of its input
integer square root
number-theoretic function: floor of the square root
prime omega function
two theoretical number functions
floor function
function that maps a real number x to the greatest integer less than or equal to x
tau-function
giving the Fourier coefficients of the Ramanujan modular form
partition function
number of partitions of an integer, often used in number theory
aliquot sum
sum of all proper divisors of a natural number
nearest integer function
function which returns the nearest integer to x; for half-integers, a rounding rule must be chosen, usually to round half-integers to the nearest even integer
ceiling function
function that maps a real number x to the smallest integer greater than or equal to x