query: Is there more than one harmonic number that is natural?
positive_passages.docid: 46946
positive_passages.text: Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
negative_passages.docid: 96303
negative_passages.text: When does $h(x^2+y^2)$ be harmonic?
negative_passages.docid: 5375
negative_passages.text: Is there a bijective function mapping Natural numbers to Natural numbers, other than $f(n) = n$?
negative_passages.docid: 28942
negative_passages.text: About Math notation: the set of the first $n$ natural numbers
negative_passages.docid: 25097
negative_passages.text: Inequalities to give bounds on generalised harmonic numbers?
negative_passages.docid: 109599
negative_passages.text: A finite sum involving the binomial coefficients and the harmonic numbers
negative_passages.docid: 153976
negative_passages.text: Do complex quantities and irrational numbers exist in nature?
negative_passages.docid: 22842
negative_passages.text: The Interpretation of $|\psi|^2$ and the No-Clone Theorem
negative_passages.docid: 130
negative_passages.text: What is a "harmonic quadruple"?
negative_passages.docid: 155951
negative_passages.text: Harmonic series sum approximation
negative_passages.docid: 156242
negative_passages.text: As many even numbers as natural numbers.
negative_passages.docid: 39771
negative_passages.text: Is the natural log of n rational?
negative_passages.docid: 146883
negative_passages.text: Physical reason behind having greater amplitude when driving frequency$ $ natural frequency
negative_passages.docid: 4530
negative_passages.text: For which natural numbers are $\phi(n)=2$?
negative_passages.docid: 66380
negative_passages.text: Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 90957
negative_passages.text: Relation between Stirling numbers of first kind and harmonic numbers