428 Digital sum and digital root
Exercise
1.A Filzian number is one which is the product of its digits and digial
sum. For example,144 = 1· 4 ·4(1+4+4). Find one more such
number.^12.Find the digital root ofn!.3.Find the digital root sequence ofn^2.4.The cubes.5.The triangular numbers.
6.Find all integersnsuch that the sum of the digits ofn^2 is equal to
n,i.e.,d(n^2 )=n.7.What is the digital root of a number of the form 2 n−^1 (2n−1)?(^1) Answer: 135. It is known that there are only finitely many Filzian numbers. Apart from 1 and 144, the
other known one is 135.