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Old 2012-05-22, 09:16   #7
Just call me Henry
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Sep 2007
Cambridge (GMT/BST)

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Originally Posted by CRGreathouse View Post
Use a weighted sum of the appropriate pi_k.

For example, if you wanted the number of odd 3-almost-primes up to x, that's pi_3(x) - pi_2(x/2).
Brilliant thanks. Wierdly I actually thought of something similar while going to sleep last night.
Does this sort of start a chain where pi_2(x/2) needs correcting by subtracting from it pi_1(x/4) etc.?
This would lead to pi_k(x)-pi_(k-1)(x/2)+pi_(k-2)(x/4)-pi_(k-3)(x/8) ... which you would continue until you have the necessary precision.
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