Let
σ
(
n
)
\sigma (n)
denote the sum of the positive divisors of
n
n
. We say that
n
n
is perfect if
σ
(
n
)
=
2
n
\sigma (n) = 2 n
. Currently there are no known odd perfect numbers. It is known that if an odd perfect number exists, then it must be of the form
N
=
p
α
∏
j
=
1
k
q
j
2
β
j
N = p^\alpha \prod _{j=1}^k q_j^{2 \beta _j}
, where
p
,
q
1
,
…
,
q
k
p, q_1, \ldots , q_k
are distinct primes and
p
≡
α
≡
1
(
mod
4
)
p \equiv \alpha \equiv 1 \pmod {4}
. Define the total number of prime factors of
N
N
as
Ω
(
N
)
:=
α
+
2
∑
j
=
1
k
β
j
\Omega (N) := \alpha + 2 \sum _{j=1}^k \beta _j
. Sayers showed that
Ω
(
N
)
≥
29
\Omega (N) \geq 29
. This was later extended by Iannucci and Sorli to show that
Ω
(
N
)
≥
37
\Omega (N) \geq 37
. This paper extends these results to show that
Ω
(
N
)
≥
47
\Omega (N) \geq 47
.