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Tagged with integer-partitions prime-numbers
6
questions with no upvoted or accepted answers
6
votes
0
answers
181
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Almost a prime number recurrence relation
For the number of partitions of n into prime parts $a(n)$ it holds
$$a(n)=\frac{1}{n}\sum_{k=1}^n q(k)a(n-k)\tag 1$$
where $q(n)$ the sum of all different prime factors of $n$.
Due to https://oeis....
- 13.9k
4
votes
0
answers
218
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Relationship between Riemann Zeta function and Prime zeta function
In his paper, Daniel Grunberg shows a relationship between the Stirling Numbers of the first kind and the Harmonic numbers via series of partitions (see Equation 3.1 on Page 5 in the link above). If ...
- 3,557
2
votes
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45
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Express number of partitions into prime numbers using partitions into natural numbers.
Let $P(n)$ is number of partitions of $n$ into natural numbers.
$R(n)$ is number of partitions of $n$ into prime numbers.
Is there any expression that relates $P(n)$ , and $R(n)$? I look for ...
- 1,382
2
votes
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937
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Is every integer $\geq5$ the sum of two primes and a power of a prime?
Is every integer $\geq5$ the sum of two primes and a power of a prime (where $1$ is included in the prime powers)?
I don't really expect someone to prove this here, but I wonder if the question has ...
- 810
0
votes
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51
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Summation of a prime and a prime power
Is there an even number $n \in \mathbb{N}$ and two different primes $p,q<n$ which are not divisors of $n$, as well as $a,b \in \mathbb{N}$ with $a,b>1$, such that
$$
n=q+p^{a}=p+q^{b}
$$
? I ...
- 21
0
votes
0
answers
40
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The number of $n\in\mathbb{N}$ with $p(n)$ is prime
Let $p(n)$ denote the number of integer partitions of $n$ for $n\in\mathbb{N}$.
Is it possible to list the cases where $p(n)$ is prime? Are such natural numbers finite (if so how to compute a bound) ...
- 4,852