Called me 3 times in the last three days, don't leave a message. I called back, and got an automated message saying it's a telemarketing company and they could remove my number from their list.

This is NCO Financial collections - one of the things they'll harass you about is defaulted student loans - they have a reputation of being cut-throat.  Can't get blood from a turnip, as they say.

Called.. i answered, the caller mentioned some magazine! Nuisance.

They have been calling our landline often lately; I don't pick up and they ring off before the answering machine answers.

They don't answer when I pick up and they don't leave a message.