Ruud H.G. van Tol on Sat, 26 Nov 2022 11:30:08 +0100

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"A071521 Number of 3-smooth numbers <= n"

The (to me very educational) PARI-code
from Charles, on that page, looks to me
like a variant of a formula shown in
the "Raphael Schumacher" link.

I would now probably write it as:
A071521(n)= my(t=1);sum(k=1,logint(n,3),logint(n\t*=3,2)+1)

(just trying to shave off another millisecond,
though I was blown away by its speed already:
a 3^k variant takes 40x as long)

-- Ruud

P.S. As n could be any ridiculous integer,
a "powers()" approach isn't applicable.
A "Power(b,e)=exp(e*log(b))" approach might be feasible,
but that probably just takes longer,
and will add precision treats.