Display graph of x versus number of prime factors of x

Question

I am trying to get wolfram alpha website to display a graph where you have x on one axis and the number of not necessarily distinct prime factors on the other axis. I tried this query: plot f(x) = number of factor x

Did not work. How can I do this? Thank you

score 3 · Accepted Answer · answered May 31 '15 at 14:16

3

After the usual lots of trial and error that WolframAlpha didn't understand, finally

WolframAlpha PrimeOmegaPlot link

answered May 31 '15 at 14:16

Bill

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+1 note you can also use `ListPlot` and camel case: `ListPlot[Table[PrimeOmega[x],{x,1,64}]]` which is then a proper mathematica expression. I would assume it cant simply `Plot[PrimeOmega..]` because its only defined for integers – agentp Jun 01 '15 at 19:37

score 2 · Answer 2 · answered May 31 '15 at 12:33

The function you are looking for is called PrimeOmega in Mathematica.

Here is the doc

http://reference.wolfram.com/language/ref/PrimeOmega.html

where you can find a plot of the first 100 values.

It used to be quite simple to just enter a correct Mathematica statement into Wolfram Alpha and get its output but not anymore in the public version. If you type PrimeOmega in Wolfram Alpha you will get its definition and the first few values in a table.

If you have access to Mathematica, use

DiscretePlot[PrimeOmega[n],{n,1,1000}]

and experiments with various options.

Plot of Prime Omega (first 1000 values)

Display graph of x versus number of prime factors of x

2 Answers2