Divisors

For integer input integer divisors are returned:

For Gaussian integer input Gaussian divisors are produced:

Divisors threads element-wise over list arguments:

This will produce Gaussian divisors for integer input:

Some primes are also Gaussian primes:

The ratio of Gaussian divisors to integer divisors:

Find all perfect numbers less than 10000:

Representation of 25 as sum of two squares:

PowersRepresentations generates an ordered representation:

Number of representations of a number as a sum of four squares:

Computation by SquaresR:

This counts the number of divisors:

In general, DivisorSigma[d, n]_k|nk^d:

Similarly, EulerPhi[n]n_p|n(1-1/p) where p is prime:

Alternatively, EulerPhi[n]n_k|nMoebiusMu[k]/k:

Divisors gives all divisors except for multiplication by units, that is, they lie in the first quadrant:

Get all divisors: