Sum of powers of all divisors of a natural number.
Sigma(n, k = 1, proper = FALSE)tau(n)
tau(n)
Positive integer.
Numeric scalar, the exponent to be used.
Logical; if TRUE, n will not be considered as a divisor of itself; default: FALSE.
TRUE
Natural number, the number or sum of all divisors.
Total sum of all integer divisors of n to the power of k, including 1 and n.
n
k
1
For k=0 this is the number of divisors, for k=1 it is the sum of all divisors of n.
k=0
k=1
tau is Ramanujan`s tau function, here computed using Sigma(., 5) and Sigma(., 11).
tau
Sigma(., 5)
Sigma(., 11)
A number is called refactorable, if tau(n) divides n, for example n=12 or n=18.
n=12
n=18
http://en.wikipedia.org/wiki/Divisor_function
http://en.wikipedia.org/wiki/Tau-function
primeFactors, divisors
primeFactors
divisors
# NOT RUN { sapply(1:16, Sigma, k = 0) sapply(1:16, Sigma, k = 1) sapply(1:16, Sigma, proper = TRUE) # }
Run the code above in your browser using DataCamp Workspace