27473 is a numbers whose arithmetic and multiplicative digital roots are not digits of the number itself but whose arithmetic root is equal to the number of digits in the number. Here the arithmetic digital root is 5 and the multiplicative digital root is 8. The number of digits in the number (5) corresponds to the arithmetic digital root. See entry to 27374 (a permutation of the digits of 25473).

Ignoring permutations, there are only 39 numbers (with digits in ascending order) in the range up to 40000 and they are (permalink):

47, 129, 147, 228, 444, 489, 669, 777, 1129, 1228, 1237, 1399, 1669, 1777, 2236, 2299, 11129, 11147, 11228, 11237, 11399, 11444, 11489, 11669, 11777, 12236, 12299, 13469, 13478, 14477, 14666, 22244, 22334, 22469, 23477, 27779, 27788, 33377, 34466

Allowing permutations there are 556 numbers up to 40000. Numbers with the digit 0 are excluded from consideration because they have a multiplicative digital root of 0 and that will always differ from the arithmetic digital root that must lie between 1 and 9.

It can be seen that the digits of 27473 is a permutation of the digits of 23477.

27473 is a d-powerful number because it can be written as 2 + 7 + 4^6 + 7^5 + 3^8.

27473 can be rendered as a digit equation as follows:

2 + 7 = (-4 + 7) * 3.