Sync Office 365 user calendar, task and attribute sync with on premise SharePoint 2013 Enterprise

So, I've looked at a lot of documentation and I don't have a clear answer with my scenario.  I DO NOT have on-premise Exchange and all email services are in Office 365.  I DO have SharePoint 2013 Enterprise on-premise.  We DO NOT use SharePoint Online.  What I want is user calendar and task synchronization (as well as user attributes like address, photo, etc) between the on-premise SharePoint 2013 server and Office 365 hosted Email.  I would prefer to not lock users into authenticating against local authentication source to get their email (I'm not looking for SSO) but want bi-directional attribute sync.

What are my options here?

Thanks,

Mark Ringo