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The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Thus d(30) =

number of such divisors=8, ľ(30) = sum of such divisors=72 and ľ2(30) =

sum of squares of such divisors= 1 + 4 + 9 + 25 + 100 + 225 + 900 = 1300.

From the formula, since 30=2.3.5, we have d(30 = (1 + 1)(1 + 1)(1 + 1) =

8; ľ(30 = 22

ˇ1

2ˇ1 : 32

ˇ1

3ˇ1 : 52

ˇ1

5ˇ1 = 3

1 : 8

2 : 24

4 = 72 and ľ2(30) = 24

ˇ1

22

ˇ1 : 34

ˇ1

32

ˇ1 : 54

ˇ1

52

ˇ1 =

15

3 : 80

8 : 624

24 = 5:10:26 = 1300.

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