Happy number

As reminder, a happy number is the number where the sequence of the sum of the squares of the digits equal 1.
For example, 1 is happy number because 1² = 1. 


7 is  a happy number because 
  7² = 49
  4² + 9² = 97
  9² + 7² = 130
  1² + 3² + 0² = 10
  1² + 0² = 1.


4 is not a happy number because

  4² = 16

  1² + 6² = 37

  3² + 7² = 58

  5² + 8²  = 89

  8² + 9² = 145

  1² + 4² + 5²  = 42

  4² + 2²  = 20

  2² + 0²  = 4

that yields an infinite loop digit sum of squares.

Here is my attempt to write happy number in Scala way.

First, I need to define sumOfSquares function, implemented as follow:

 1 def sumOfSquares(n: Int): Int = {
 2   def sumOfSquares(n: Int, powOf10: Int, acc: Int): Int = {
 3     if ( n / powOf10 == 0) {
 4       acc
 5     }
 6     else {
 7       val digit = (n / powOf10) % 10
 8       val result = acc + digit * digit 
 9       sumOfSquares(n, powOf10 * 10, result)
10     }
11   }
12   sumOfSquares(n, 1, 0)
13 }
14     

The function calls an inner method sumOfSquares that is a recursive function, taking into account that the sumOfSquares of an integer is the square of its last digit + the sumOfSquares the rest of the digits. 
The isHappyNumber function is then defined as follow:

14

15 def isHappyNumber(n: Int) = {
16   def isHappyNumberList(n: Int, lst: Set[Int]): Boolean = {
17     sumOfSquares(n) match {
18       case 1 => true
19       case sum => !lst.contains(sum) && isHappyNumberList(sum, lst + n)  
20     }
21   }
22   isHappyNumberList(n, Set.empty)
23 }
24 

That is, if the sum of squares of n is 1, then n is a happy number, otherwise n is a happy number when its sum of squares is a happy number given the sequence of the sum of squares does not yield an infinite loop.
To detect an infinite loop, a set of calculated sum of squares is kept and for each new generated sum, the program verifies that the number is not in the set already.