On divisibility by 27

Notation. We denote the sum of the digits of a positive integer n by SD(n). The notation a | b means: ‘a is a divisor of b’, i.e., ‘b is a multiple of a.’ Throughout, we work in base 10. Two well-known statements. The following two statements are very well-known: (1)A positive integer n is divisible by 3 if and only if SD(n) is divisible by 3. (2)A positive integer n is divisible by 9 if and only if SD(n) is divisible by 9