galois.divisor_sigma

galois.divisor_sigma(n: int, k: int = 1) → int

Returns the sum of $k$ -th powers of the positive divisors of $n$ .

Parameters:¶

n: int¶: An integer.
k: int = 1¶: The degree of the positive divisors. The default is 1 which corresponds to $σ_{1} (n)$ which is the sum of positive divisors.

Returns:¶

The sum of divisors function $σ_{k} (n)$ .

See also

factors, divisors

Notes

This function implements the $σ_{k} (n)$ function. It is defined as:

σ_{k} (n) = \sum_{d | n} d^{k}

Examples

In [1]: galois.divisors(9)
Out[1]: [1, 3, 9]

In [2]: galois.divisor_sigma(9, k=0)
Out[2]: 3

In [3]: galois.divisor_sigma(9, k=1)
Out[3]: 13

In [4]: galois.divisor_sigma(9, k=2)
Out[4]: 91