SOGL V0.12, 14 bytes

1[:Λ∑:A.>?ao←I

Try it Here!

SOGL V0.12, 14 bytes

1[:Λ∑:A.>?ao←I

Try it Here!

Explanation:

1 push 1
 [ while ToS != 0
 :Λ get the divisors
 ∑ sum
 :A save on variable A without popping
 .>? ← if greater than the input
 ao output the variable A
 ← and stop the program, implicitly outputting ToS - the counter
 I increment the counter