Difference between revisions of "Sum of divisors"
From specialfunctionswiki
(Created page with "The sum of positive divisors function, $\sigma_x$, is defined by $$\sigma_x(n) = \displaystyle\sum_{d|n} d^x,$$ where $d|n$ denotes that $d$ is a divisor of $n$.") |
|||
| (7 intermediate revisions by the same user not shown) | |||
| Line 2: | Line 2: | ||
$$\sigma_x(n) = \displaystyle\sum_{d|n} d^x,$$ | $$\sigma_x(n) = \displaystyle\sum_{d|n} d^x,$$ | ||
where $d|n$ denotes that $d$ is a [[divisor]] of $n$. | where $d|n$ denotes that $d$ is a [[divisor]] of $n$. | ||
| + | |||
| + | =Properties= | ||
| + | [[Sum of divisors functions written in terms of partition function]]<br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1}}: $24.3.3 I.A.$ | ||
| + | |||
| + | {{:Number theory functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 20:50, 26 June 2016
The sum of positive divisors function, $\sigma_x$, is defined by $$\sigma_x(n) = \displaystyle\sum_{d|n} d^x,$$ where $d|n$ denotes that $d$ is a divisor of $n$.
Properties
Sum of divisors functions written in terms of partition function
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.3.3 I.A.$
