Cool ProblemNumber Theory Level 3
Let \(f(n)\) denote the sum \(1+2+3+...+(n−1)+n\). Let \(g(n)\) denote the sum \(1+3+...+k\), where \(k\) is the \(n\)th positive odd number. There are \(x\) integers n such that \(1≤n≤100\) and \(2f(n)−g(n)\) is divisible by both \(3 \)and \(2\). What is the sum of the digits of \(x\)?