Integers n; sum of the reciprocals of prime factors + 1/n = 1

Allowing prime powers among the divisors

k = 7,    n = 144508961850
$144508961850 \; = \; 2\cdot 3\cdot 5^2\cdot 11\cdot 29\cdot 1097\cdot 2753$
Prime factors :    (2,3,11,25,29,1097,2753)
The sum of the reciprocals (S) is,
1/2 + 1/3 + 1/11 + 1/25 + 1/29 + 1/1097 + 1/2753 = 144508961849/144508961850
(S) + 1/n = 144508961849/144508961850 + 1/144508961850 = 1

k = 8,    n = 20882840055109264384350
$20882840055109264384350 \; = \; 2\cdot 3\cdot 5^2\cdot 11\cdot 29\cdot 1097\cdot 2753\cdot 144508961851$
Prime factors :    (2,3,25,11,29,1097,2753,144508961851)
The sum of the reciprocals (S) is,
1/2 + 1/3 + 1/25 + 1/11 + 1/29 + 1/1097 + 1/2753 + 1/144508961851
= 20882840055109264384349/20882840055109264384350

(S) + 1/n =
= 20882840055109264384349/20882840055109264384350 + 1/20882840055109264384350 = 1

Is there a solution with 9 prime factors?