# numDivisorSieve: Apply Divisor Function to Every Element in a Range In RcppAlgos: High Performance Tools for Combinatorics and Computational Mathematics

 numDivisorSieve R Documentation

## Apply Divisor Function to Every Element in a Range

### Description

Sieve that generates the number of divisors for every number between bound1 and bound2 (if supplied) or all numbers up to bound1. This is equivalent to applying the divisor function (often written as \sigma(x)) to every number in a given range.

### Usage

numDivisorSieve(bound1, bound2 = NULL, namedVector = FALSE, nThreads = NULL)


### Arguments

 bound1 Positive integer or numeric value. bound2 Positive integer or numeric value. namedVector Logical flag. If TRUE, a named vector is returned. The default is FALSE. nThreads Specific number of threads to be used. The default is NULL.

### Details

Simple and efficient sieve that calculates the number of divisors for every number in a given range. This function is very useful when you need to calculate the number of divisors for many numbers.

This algorithm benefits greatly from the fast integer division library 'libdivide'. The following is from https://libdivide.com/:

• libdivide allows you to replace expensive integer divides with comparatively cheap multiplication and bitshifts. Compilers usually do this, but only when the divisor is known at compile time. libdivide allows you to take advantage of it at runtime. The result is that integer division can become faster - a lot faster.

### Value

Returns a named/unnamed integer vector

### Note

The maximum allowed value is 2^{53} - 1.

Joseph Wood

### Examples

## Generate some random data
set.seed(8128)
mySamp <- sample(10^6, 5*10^5)

## Generate number of divisors for
## every number less than a million
system.time(mySigmas <- numDivisorSieve(10^6))

## Now use result in algorithm
for (s in mySamp) {
sSig <- mySigmas[s]
## Continue algorithm
}

## Generating number of divisors for every
## number in a range is no problem
system.time(sigmaRange <- numDivisorSieve(10^13, 10^13 + 10^6))

## Returning a named vector
numDivisorSieve(10, 20, namedVector = TRUE)
numDivisorSieve(10, namedVector = TRUE)