Talk:Smooth number

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[edit] Powersmooth example

The powersmooth example is correct, though the number is also 16-powersmooth, which is more useful. 2^4 <= 16 I'm new to wikipedia or else I might just change it. User:Erg255

Thanks, yes. I changed it. --Nuffle 14:33, 9 November 2005 (UTC)

[edit] Formula for 3-smooth sequence

Is there a formula for the n th number in the 3-smooth sequence? User:SurrealWarrior

Not that I know of. A003586 has an asymptotic formula, though. CRGreathouse (t | c) 19:19, 12 September 2007 (UTC)

[edit] Is the distribution formula correct?

The distribution is given as approximately

\Psi(x,B) \sim \frac{1}{\pi(B)!} \prod_{p\le B}\frac{\log x}{\log p} .

which is equivalent to

\Psi(x,B) \sim \prod_{p_i\le B}\frac{\log x}{i\log p_i} .

(counting i from 1)

Each term in the product marks how much adding that term increases the number of B-smooth numbers below x. But the terms can fall below one, which means that the estimate for Ψ(x,B) can go down as B increases, which makes no sense.

Can anyone explain? — ciphergoth 17:48, 17 February 2007 (UTC)

That asymptotic formula is only true for B small (relative to x). Only large values of B cause trouble there. CRGreathouse (t | c) 19:18, 12 September 2007 (UTC)