Using a mathematical identity to speed up certain calculations.

[ColinE66]

re post #10, I can see that you are going to have great difficulty avoiding subtracting the same numbers more than once when different multiples 'intersect'. I assume that is what you are struggling to resolve...

[Schmidt]

re post #10, I can see that you are going to have great difficulty avoiding subtracting the same numbers more than once when different multiples 'intersect'. I assume that is what you are struggling to resolve...

Yep - I'm trying to find a generic function which internally makes use of the O(1)-category n*(n+1)/2 approach,
to avoid the O(n) looping over the whole range.

Not sure, if your function in #12 really does speed-up what I posted in #8,
since I already had an early exit there, as soon as a valid factor was found
(not possible to count something twice).

When you use my function in #8 with n-1 as the parameter, then it wil always produce
the same results as yours for the same list of PrimeFactors.

Olaf