I have developed an algorithm, Sieves like, that only pick every integer once. The Sieve algorithm of course selecting integers in as many iterations as the integer has distinct prime factors. 


Is this seen before (I haven't found it) ? 



Sieve algorithm that only pick every integer once?
It may interest you that the asymptotically fastest prime sieve (of Atkin-Bernstein) spends less than unit time on each number in the interval, by considering increasingly thin congruence classes as its input increases. (Of course it spends positive time, $O(\log n/\log\log n)$, on each *prime*.)


