Author 
Comment/Response 
JD

07/08/13 6:42pm
In Response To 'Re: Solving for when a summation reaches a value.'  I tried it on my computer and the graph I came up with is a simple x=y graph. Maybe if the y side of the graph was the LCM (1,2,...n)and the x side of the graph was n, I could get a ballpark estimate.
I looked into the reference you gave for Mathworld. I had been there long ago, but I did see that
Psi(n)= ln(LCM(1,2,3,...,n)
so if I understand logs correctly, then
E^[Psi(n)]= (LCM(1,2,3,...,n)
and then the following should give me the number of digits of the LCM
In[]:= Solve[3 <= Ceiling[log[E^(\[Psi] (n))]] && n > 0, n ][[1]]
During evaluation of In[]:=
Solve::nsmet : "This system cannot be solved with the methods \
available to Solve. \!\(\*ButtonBox["\[RightSkeleton]",
Appearance>{Automatic, None},
BaseStyle>"Link",
ButtonData:>"paclet:ref/Solve",
ButtonNote>"Solve::nsmet"]\)"
Out[]= 3 <= Ceiling[log[E^(n \[Psi])]] && n > 0
Ceiling[log[E^(\[Psi] (9))]]
During evaluation of In[38]:=
Syntax::tsntxi : "\"\[NoBreak][Ceiling[log[\[ExponentialE]^(\[Psi] \
(9))]]]\[NoBreak]\" is incomplete; more input is needed.\[NoBreak]""\
\[NoBreak]"
During evaluation of In[38]:=
Syntax::sntxi : "Incomplete expression; more input is needed \
\[NoBreak]""\[NoBreak]."

Okay, so I'm giving the computer really simply stuff and it just gives it back to me with the last entry.
Since I am so new to Mathematica, I assume that there has to be something completely basic that I am not doing.
I can't even get it to
Evaluate[ã^(y(9))]
I am using a notebook, .nb file. I right click on the cell after I'm finished and use Evaluate Cell. Nothing is happening.
I should have got an answer of e^2520 or some number. If this thing doesn't put out soon, I'm going to explode.
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