Amen! Repentance is a "change of mind" and not a work for salvation. The Greek word for "repent" is "metanoia" (noun) and "matanoeo" (verb) you see as defined in the Strongs #3340, 3341:
to think differently or afterwards, reconsider. After thought, change of mind.
Repentance basically means a "change of mind" and the context must determine what is involved in this change of mind. Where salvation is in view, repentance actually precedes saving faith in Christ and is not a totally separate act from faith. It is actually the same coin with two sides. Repentance is on one side (what you change your mind about) and faith in Christ is on the positive side, (the new direction of this change of mind). Repentance and faith are two sides of the same experience of receiving Christ.
In the context of Luke 13:3, Jesus challenged the people's notion that they were morally superior to those who suffered in such catastrophes. He called all to
repent or perish. For some people though, prior to coming to the end result of repentance (changing our mind) in receiving salvation (faith in Christ), they must change their minds about other specific things in order to get there. Repentance, metanoia, focuses on changing one's mind about his previous concept of God (as in Acts 17:30) and disbelief in God or false beliefs (polytheism and idolatry) about God (1 Thessalonians 1:9). On the other hand, this change of mind, focuses on the new direction that change about God must ultimately take, namely, trusting in Jesus Christ alone for salvation.
The Bible also tells us that true repentance will
result in a change of actions. Acts 26:20 declares, "I preached that they should repent and turn to God and
prove their repentance by their deeds." This is the
fruit of repentance (Matthew 3:8) and not the essence of repentance (change of mind). Certain people confuse the "fruit of repentance" with the "essence of repentance" (and also do the same thing with faith) and end up teaching salvation by works. All genuine believers are fruitful, yet not all are equally fruitful. (Matthew 13:23)
Matthew 7:21 - Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who
does the will of My Father in heaven.
John 6:40 - For
my Father’s will is that everyone who looks to the Son and
believes in him shall have eternal life, and I will raise them up at the last day.