Difference between revisions of "Recurrence relation for partition function with sum of divisors"
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Latest revision as of 20:43, 26 June 2016
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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.2.1 \mathrm{II}.A.$
