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(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 4digit numbers, Kaprekar’s constant, namely, 6174, has an anagrammatic totient, namely, 1764 (which, incidentally, is the year of Goldbach’s death).