notificationstwitter
On Twitter – I don't want notifications whenever someone likes my tweet, or likes tweets that I'm mentioned in.
However, I do want to be notified when someone replies to my tweets.
I want these settings to apply for what is known as the 'notifications timeline' in Twitter's terminology, ie notifications within the desktop browser application.
Is this possible to set up?
One method would be to automatically retweet everything by the one account. A quick web search shows that there are multiple ways of accomplishing this. One way is using Yahoo! Pipes. (An example of how to do that: http://hubpages.com/hub/How-to-automatically-retweet-on-Twitter-using-Yahoo-Pipes-and-Twitterfeed-auto-RT-explained)
Not exactly selective but, TweetDelete has a nifty feature of allowing you to delete tweets older that a specified age. This makes it easier to get rid of the older tweets that might take a long time to scroll through and manually delete with Twitter's web UI.
Best Answer
Disable "Liked" notifications for Web and Browser
NOTE: Although the same can be done for notifications on mobile devices, there is no way to filter the Notifications timeline that specifically. You can only filter words or accounts from your Notifications timeline, according to the Twitter help page About the Notifications timeline (subheading Can I filter the notifications I receive?)