  We extend to Segal-Piatetski-Shapiro sequences previous results on the
Luca-Schinzel question over integral valued polynomial sequences. Namely, we
prove that for any real $c$ larger than $1$ the sequence $(\sum_{m\le n}
\varphi(\lfloor m^c \rfloor) /\lfloor m^c \rfloor)_n$ is dense modulo $1$,
where $\varphi$ denotes Euler's totient function. The main part of the proof
consists in showing that when $R$ is a large integer, the sequence of the
residues of $\lfloor m^c \rfloor$ modulo $R$ contains blocks of consecutive
values which are in an arithmetic progression.
