Lemma.
If
x
≥
1
, then
∑
n
≤
x
1
n
=
log
x
+
γ
+
O
(
1
x
)
,
where
γ
∈
ℝ
is Euler’s constant, which is given by
γ
=
lim
N
→
∞
∑
k
=
1
N
1
k
−
log
N
.