Dear Mike.
I gratefully accept the rebuke.
I disagree with you, when you write, that you'll get slow in Mathematica if
you step outside the standard library.
I've shown several times that it is absolutely possible to beat built-ins.
If I had to come up with my own DivisorSigma,
I'd go with something like:
divsigma = Compile[{{lim, _Integer}}, Module[{dsum}, dsum = Table[1, {lim}];
Do[dsum[[k]] += n, {n, 2, lim}, {k, n, lim, n}];
dsum], RuntimeOptions -> "Speed", CompilationTarget -> "C"];
This is already faster than the built-in.
preallocating an array of divisor sums up to e.g. 9999 an rewriting
AmicableQ:
ds = divsigma[9999];
AmicableQ[n_Integer] := Block[{sum = ds[[n]] - n},
sum != n && ds[[sum]] - sum == n
]
and selecting those numbers from the range:
Plus @@ Select[Range[2, 9999], AmicableQ] // Timing
yields the correct result in 0.68s and memory usage of 238464B, although
this can be very misleading, since it is not absolutely clear how much
memory
really was needed, since the notebook may've introduced new stuff
during calculation (I consider this as another weak point of Mathematica).
What I take away from this thread is, that Julia is very impressing indeed
and I'm very
glad that from now on I do have the opportunity to switch over from
Mathematica,
especially when it is driving me mad, which happens quite oftenly ;)
I do not have a problem with the fact, that the standard library is not
filled with everything I may
need at some particular point.
Once again.
Thank you all for the replies, that was rather enlightening.
Cheers
Stefan
