View source for Sum of divisors functions written in terms of partition function

==Theorem==
The following formula holds:
$$\sigma_1(n)=p(n)+\displaystyle\sum_{1 \leq \frac{3k^2 \pm k}{2} \leq n} (-1)^k\dfrac{3k^2 \pm k}{2} p \left(n - \dfrac{3k^2 \pm k}{2} \right),$$
where $\sigma_1$ denotes the [[sum of divisors]] function and $p$ denotes the [[partition function]]. 

==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Recurrence relation for partition function with sum of divisors|next=Asymptotic formula for partition function}}: $24.2.1 \mathrm{II}.B.$

[[Category:Theorem]]
[[Category:Unproven]]