Let
ω
(
n
)
\omega (n)
be the number of distinct prime factors of
n
n
. For any positive integer
k
k
let
n
=
n
k
n=n_k
be the smallest positive integer such that
ω
(
n
+
1
)
,
…
,
ω
(
n
+
k
)
\omega (n+1),\ldots ,\omega (n+k)
are mutually distinct. In this paper, we give upper and lower bounds for
n
k
n_k
. We study the same quantity when
ω
(
n
)
\omega (n)
is replaced by
Ω
(
n
)
\Omega (n)
, the total number of prime factors of
n
n
counted with repetitions.