Prefix Sums of Multiplicative Functions

https://codeforces.com/blog/entry/54150

Linear Time Sieve

https://judge.yosupo.jp/problem/enumerate_primes

Counting Primes

https://judge.yosupo.jp/problem/counting_primes

Totient Function

https://judge.yosupo.jp/problem/sum_of_totient_function

Copy
template<int SZ> struct Sieve {
	vi pr;
	int sp[SZ], phi[SZ]; // smallest prime that divides
	Sieve() { // above is faster
		memset(sp,0,sizeof sp);
		phi[1] = 1;
		FOR(i,2,SZ) {
			if (sp[i] == 0) {
				sp[i] = i, pr.pb(i); phi[i] = i-1;
			} trav(p,pr) {

(project euler)

(topcoder problem)