On a conjecture of Goldmakher

We construct a $1$-bounded completely multiplicative function $f$ whose logarithmically-averaged partial sums satisfy $$\underset{x\to \mathrm{\infty }}{\mathrm{lim\hspace{0.17em}sup}}\frac{\mid \sum _{n\le x}\frac{f(n)}{n}\mid }{1+\exp \left(\sum _{p\le x}\frac{\text{Re}(f(p))}{p}\right)}=\mathrm{\infty }\mathrm{.}$$ This disproves a conjecture of Goldmakher from 2009.