Just received a call from this number---Called ID showed HEALTHCARE----I did not answer, because I already have a Healthcare Program....................

See above.  The same.

Saw the number on my caller ID.  No message.  Whatever.

Rang 4 or 5 times and they hung up, no voice message. Called number back, rang  a few times then: auto-operator said "THIS NUMBER HAS A VOICE MAIL THAT HASN'T BEEN SET UP." Same story when I called back a couple of times more.

The calls, they don't stop, 16 more this week.  A few new numbers, but notice the similar times and number calling patterns to my previous updates:

480-214-2884 @ 2013-05-13 10:52am - HIGHLANDS
602-867-0957 @ 2013-05-13 03:20pm - PHOENIX,AZ
602-674-1033 @ 2013-05-13 05:00pm - No Caller ID Name
601-474-3298 @ 2013-05-14 09:20am - ONE LIFE AMERIC
855-501-2364 @ 2013-05-14 12:50pm - TOLL FREE
602-903-6849 @ 2013-05-14 03:52pm - WIRELESS CALLER
480-214-2884 @ 2013-05-14 07:24pm - HIGHLANDS
323-960-3543 @ 2013-05-14 08:45pm - CA
205-440-3884 @ 2013-05-15 08:37am - HEALTHCARE (new for me)
480-894-9342 @ 2013-05-15 06:35pm - HIGHLANDS
813-426-8822 @ 2013-05-15 06:40pm - No Caller ID Name
602-903-6849 @ 2013-05-15 06:57pm - WIRELESS CALLER
602-903-6849 @ 2013-05-16 06:33pm - WIRELESS CALLER
480-894-9342 @ 2013-05-16 07:53pm - HIGHLANDS
480-335-9842 @ 2013-05-16 08:03pm - No Caller ID Name (new for me)
618-551-5619 @ 2013-05-17 10:07am - DEPPROCCESSING (new for me)

I suspect these calls may be part of the same scam organization that stuck my number in their auto-dialer 14 months ago and has been harassing me ever since.  More detail and numbers that have been bombarding me with calls are listed in my posts here:

http://800notes.com/Phone.aspx/1-920-560-4999/7

I have gotten a recorded call several times in the last week;  say it is the Alzheimers Association and to
push a number to find out how they can help me.  Unsolicited!

got a call from this number, I let it go to the answer machine then called back. The only mess I got was to press any number to be removed from calling list. It much be some sort of marketing scam or spoof.
Spoof is illegal: The Truth in Caller ID Act of 2009, which was signed into law Dec. 22, 2010, prohibits caller ID spoofing for the purposes of defrauding or otherwise causing harm. In June 2010, the Federal Communications Commission adopted rules implementing the Truth in Caller ID Act.
check http://www.fcc.gov/guides/caller-id-and-spoofing