(or, ‘anagrammatic totients’ for short)
(suggested new terminology)
Definition. For numbers of a specified number of digits (padding with leading zeros if necessary), an anagrammatic totient value (or, an anagrammatic totient, for short) is a totient that is an anagram of the argument.
For example, for 4-digit numbers, Kaprekar’s constant, namely, 6174, has an anagrammatic totient, namely, 1764 (which, incidentally, is the year of Goldbach’s death).