Cipher with OAEPPadding and OAEPParameterSpec can't be created

According to the Cipher section of the Standard Algorithm Names document (http://docs.oracle.com/javase/7/docs/technotes/guides/security/StandardNames.html#Cipher), you can specify a padding as OAEPPadding and initialize it with an OAEPParameterSpec for the digest and mgf components. However, this doesn't work with the Oracle SunJCE provider, you get a NoSuchAlgorithmException before you can initialize the Cipher with the OAEPParameterSpec:

Exception in thread "main" java.security.NoSuchAlgorithmException: Cannot find any provider supporting RSA/ECB/OAEPPadding
at javax.crypto.Cipher.getInstance(Cipher.java:535)