After discussing with a native English speaker I accept that my translation "I want a man to rely on" has a slightly different meaning to it than "count on" does; "rely" indicates a neediness, which "count on" doesn't.
Well, my native Swedish friend says this sentence is Grammarly correct. But nobody would say like that. It's really weird. Either you mean you want to have someone to count math problem with, or you should say "Jag vill ha en man att lita på".
I am sorry, but your friend is wrong. It's a perfectly normal phrase, even if your friend does not use it. Besides, att lita på and att räkna med do not mean the exact same thing, though they are similar.
Well, to you to! The sentence in Swedish "Jag vill ha en man att räkna med" Has the meaning of both that the man in need should be reliable (to me | to others), or that he be a man of stature, highly regarded aka "to be reckoned with".
So again back to my original question!