gives the divisor function .
Details and Options
- DivisorSigma is also known as the divisor function or sum‐of‐divisors function.
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- DivisorSigma[k,n] is the sum of the k powers of the divisors of n.
- For a number with a unit and primes, DivisorSigma[k,n] returns .
- With the setting GaussianIntegers->True, DivisorSigma includes divisors that are Gaussian integers.
- DivisorSigma[k,m+In] automatically works over Gaussian integers.
Examplesopen allclose all
Basic Examples (2)
Plot DivisorSigma with log-scaled values:
Numerical Manipulation (4)
Basic Applications (3)
Special Sequences (4)
Recognize highly composite numbers: [more info]
Number Theory (6)
Properties & Relations (6)
DivisorSigma is the sum of the powers of the divisors:
Use DivisorSum to find the sum of divisors:
DivisorSigma is a multiplicative function:
Use DivisorSigma to find the product of divisors: