source("../R/friendly_numbers.R") source("../R/factorial_loop.R")
numpack99 offers access to a selection of functions to work with numbers.
In particular the following: amicable numbers perfect numbers * proper divisors
In number theory a perfect number is a positive integer number which is also equivalent to the sum of its proper divisors.
Proper divisors are all the divisors of a positive integer number except the number itself. For example the proper divisors of 4680 are:
divisors(4680)
Their sum is:
sum(divisors(4680))
The function to assess whether a number is perfect is:
perfect_number(4680)
One way to see the perfect numbers between 1 and 1000 is as follows:
x <- 1:1000 x[sapply(x, perfect_number)]
Two positive integer numbers A and B are called amicable if the sums of the proper divisors of A is equal to B and the sums of the proper divisors of B is equal to A.
The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).
The function friendly_numbers allows you to test whwther two numbers are amicable or friendly.
friendly_numbers(220, 284) friendly_numbers(17296, 18416) friendly_numbers(172960, 184160)
Additionally the package provides a function to calculate factorials implemented as a loop.
To use it:
factorial_loop(10)
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