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Feb
9
comment Counting squarefree 3-almost primes. (Solved!)
Thats an interesting library to know about I'll definitely look into it.
Feb
6
comment Counting squarefree 3-almost primes. (Solved!)
So I've checked your function for a range of values and it does appear to be counting the right things. Interestingly in my mathematica implementations (using a ParallelSum on 8 cores) your function seems to take a lot longer to evaluate for $n = 10^{10}$ and higher which was the range I was working in.
Feb
6
comment Counting squarefree 3-almost primes. (Solved!)
For $n=10^{13}$ I get $1860310801454$. Figured I'd include this for anybody else that wants to test their functions.
Feb
6
comment Counting squarefree 3-almost primes. (Solved!)
So what I was trying to count is numbers of the form $p_1p_2p_3$ with distinct $p_i$. For 50,100,150,200 I get 2,5,11,19. Counting numbers with 3 (not necessarily distinct) prime factors is given by the $\pi_3$ function. In my answer I provide a summation that subtracts the count of numbers with three prime factors that are not square free.
Feb
2
comment Can you derive a formula for the semiprime counting function from the prime number theorem?
Thanks for replying I actually created a separate question about this and later posted a solution to it after some research. It wasn't as clean as these functions but it did the job.
Feb
1
answered Counting squarefree 3-almost primes. (Solved!)
Feb
1
revised Counting squarefree 3-almost primes. (Solved!)
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Feb
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revised Counting squarefree 3-almost primes. (Solved!)
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Feb
1
revised Counting squarefree 3-almost primes. (Solved!)
add formula that I think works.
Feb
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revised Counting squarefree 3-almost primes. (Solved!)
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Feb
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revised Counting squarefree 3-almost primes. (Solved!)
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Feb
1
asked Counting squarefree 3-almost primes. (Solved!)
Feb
1
comment Can you derive a formula for the semiprime counting function from the prime number theorem?
Where did you find the exact formulas? Also do you happen to know if they can be extended to numbers of the form $n=p_1p_2p_3$ squarefree?
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Oct
12
suggested rejected edit on Evaluate the integral $\int_{1}^{4} w/(w-3) dw$ if possible
Oct
11
revised Monotone convergence of a bounded set.
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