3^k performance

A022330_1(n)=1+n+sum(k=1,n,logint(3^k,2))

A022330_2(n)=my(t=1);1+n+sum(k=1,n,logint(t*=3,2))

? A022330_1(10^5)
cpu time = 8,322 ms, real time = 8,352 ms.
%15 = 7924941755

? A022330_2(10^5)
cpu time = 215 ms, real time = 217 ms.
%16 = 7924941755


So about a 40x difference.


Is that worthwhile to look into?
How to best approach that?


BTW, I learned the trick from
https://oeis.org/A071521
(Charles R Greathouse IV, 2018)

-- Ruud

P.S. And on pari-users I would probably have
also asked which sumnum it should use. :)