In[]:=
(*mathematica*)
In[]:=
Clear[s,n,m,p,q]
In[]:=
(*Moranself-similarrationalintegerandpowersfunction*)
In[]:=
s[n_,m_,p_,q_]=N[Log[n^p]/Log[m^q]]
Out[]=
Log[
p
n
]
Log[
q
m
]
In[]:=
FullSimplifyExpandAll
Log[
p
n
]
Log[
q
m
]

Out[]=
Log[
p
n
]
Log[
q
m
]
In[]:=
lst=Union[Join[Union[Flatten[Table[Table[Table[Table[N[s[n,m,p,q]],{m,n,10}],{n,2,10}],{q,1/p,1,1/10}],{p,1,5}]]],Union[Flatten[Table[Table[Table[Table[N[s[n,m,p,q]],{m,n,10}],{n,2,10}],{p,1,5}],{q,1,10}]]]]];
In[]:=
Length[lst]
Out[]=
2053
In[]:=
Max[lst]
Out[]=
25.
In[]:=
Min[lst]
Out[]=
0.030103
In[]:=
Max[lst]/Min[lst]
Out[]=
830.482
In[]:=
ListPlot[lst,PlotStyle{Red,PointSize[0.001]},ImageSizeFull,PlotRangeAll]
Out[]=
500
1000
1500
2000
5
10
15
20
25