https://codeforces.com/blog/entry/54090

The blog presents a variant that uses a bool array instead oflp, so the space disadvantage over the Sieve of Eratosthenes is mitigated.

More helpfully, the linear sieve can be modified to compute the range [1,n] of multiplicative function, including Möbius and totient functions (although it's quite easy to modify the sieve of eratosthenes using euler's product formula to calculate totients in range)