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Fungrim entry: 4d2e45

p(n)=1nk=0n1σ1 ⁣(nk)p(k)p(n) = \frac{1}{n} \sum_{k=0}^{n - 1} \sigma_{1}\!\left(n - k\right) p(k)
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
p(n) = \frac{1}{n} \sum_{k=0}^{n - 1} \sigma_{1}\!\left(n - k\right) p(k)

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
PartitionsPp(n)p(n) Integer partition function
Sumnf(n)\sum_{n} f(n) Sum
DivisorSigmaσk ⁣(n)\sigma_{k}\!\left(n\right) Sum of divisors function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(PartitionsP(n), Mul(Div(1, n), Sum(Mul(DivisorSigma(1, Sub(n, k)), PartitionsP(k)), For(k, 0, Sub(n, 1)))))),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC