Why am I asked to install Java even after installing the latest Java version, after upgrading OS X version?

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After I updated to macOS Sierra (10.12), El Capitan (OS X 10.11) or Yosemite (OS X 10.10), why am I continually prompted to install Java again?

This article applies to:

Platform(s): macOS

SYMPTOMS

Even after upgrading to the latest version of Java, while running some applications on macOS Sierra (10.12), El Capitan (OS X 10.11), or Yosemite (OS X 10.10), users see a dialog box prompting to download Java.

macOS Sierra 10.12 or Yosemite (OS X 10.10) message:

To open "application" you need to install the legacy Java SE 6 runtime.

El Capitan (OS X 10.11) message:

To use the "java" command-line tool you need to install a JDK

CAUSE

This is most commonly because an application requires the legacy Java 6 provided by Apple. For the solution to this issue, see http://support.apple.com/kb/DL1572.