Re 1800 006 932 and 1800 465 467
I did have a similar situation as R Dojcinovic about 18 months ago (Oct 2016). I did give them remote access and paid them quite a bit of money and got what looked like a a good contract and an ongoing subscription and they seemed to have fixed the problem. Subsequently, when talking to legit Apple support about a further problem in upgrading my operating system I told them about what happened. They fixed that issue but also said that the other company was not them. They found a link to the other company in my computer, which they removed. Last night I had a call from an unknown number, saying they were from Apple Support, as they did originally, and that they had been trying to send me an email about a security risk and update and that my Apple Care subscription had run out, but the email was bouncing (presumably because of the action Apple Support proper had taken). I was talking to Apple Support proper 2 days ago and they were going to ring me back about a completely different issue, so initially I thought it was a legitimate phone call. However, the legitimate Apple person had had no trouble contacting me and had not mentioned any subscription expiring. I was suspicious pretty well straight away and refused to let them into my computer. The woman gave me a number to ring back in Australia, 1800 465 467, which wasn't the number I contacted the legitimate Apple on 2 days ago. She then gave me another number 1800 006 932 and said to ask for Sandra Jones. I said I would but didn't. They may be another legit IT company trying to get some of the apple market, but Apple Support proper have been helping me without charge about several issues and haven't mentioned any subscriptions, so if I have any alarms of the kind mentioned and ph number mentioned by R Dojcinovic, I will not be ringing it. (RW January 2018)

This was a strange no. I had a message come up on my apple mac that said my computer had been infected and apple had blocked it and to ring this number immediately. I did so and was told the sites I had been on had infected it and my computer was at risk of crashing. They sent me a code and gained remote access. I was not comfortable as when I first rang they did not answer as Apple. She could give me the serial number of my computer and also details. I had a half hour argument with her as she said I had to get the remote technicians to fix it at a cost of $150 per year subscription. I was very angry as I was given no choice as my computer had been blocked and I needed it. I relented and gave my credit card details but did not feel good about it.
She sent me a contract online stating they would fix it and I had one years subscription.
In the meantime I found a comment on reverse australia (using my iphone while I argued with her) stating the same thing happened to them (only they were microsoft) stating it was not legit. yes I think they fix your computer but they block it in the first place.
When I read the message to her and told her I changed my mind and would go to apple instead she in hast went through my computer to delete the contract, no longer argued with me and said goodbye.
I then had to ring my credit card company to cancel my card. miraculously, once I said I was going to apple and she hastily hung up, my computer was no longer blocked. but I have had to change passwords.

Bogus number linked to Microsoft scam: 'Anna Smith', with an Indian accent