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Let $f(n) = n^{\log n}$. Then $\mathsf{P} \subseteq \mathsf{DTIME}(f(n))$ while $\mathsf{DTIME}(f(2n+1)^3) \subseteq \mathsf{EXP}$. (Actually, whether this argument works depends on the exact definition of $\mathsf{DTIME}$. If it doesn't, take $f_C(n) = Cn^{\log n}$ and sum over all integer $C>0$.)


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