View source for Recurrence relation for partition function with sum of divisors

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

==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Pure recurrence relation for partition function|next=Sum of divisors functions written in terms of partition function}}: $24.2.1 \mathrm{II}.A.$

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