Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The denominators of harmonic numbers   The denominators $d_n$ of the harmonic number
$1+\frac12+\frac13+\cdots+\frac1n$ do not increase monotonically with~$n$. It
is conjectured that $d_n=D_n={\rm LCM}(1,2,\ldots,n)$ infinitely often. For an
odd prime $p$, the set $\{n:pd_n|D_n\}$ has a harmonic density and, for
$2<p_1<p_2<\cdots<p_k$, there exists $n$ such that $p_1p_2\cdots p_kd_n|D_n$.

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc