Question 12
A number is called “IMSO2” if it can be written as the sum of 2 consecutive positive integers. A number is called “IMSO3” if it can be written as the sum of 3 consecutive positive integers. A number is called “IMSO4” if it can be written as the sum of 4 consecutive positive integers. A number is called “IMSO5” if it can be written as the sum of 5 consecutive positive integers. For example, the number 15 is an IMSO2 because it can be written as 15 = 7 + 8. Moreover, 15 is also an IMSO3 because it can be written as 15 = 4 + 5 + 6. Furthermore, 15 is also an IMSO5 because it can be written as 15 = 1 + 2 + 3 + 4 + 5. However, 15 is not an IMSO4 because it cannot be written as the sum of 4 consecutive positive integers. From 1 to 2022, how many of them are IMSO2, IMSO3 and IMSO5 but not IMSO4 at the same time?