%I #15 Sep 08 2023 22:49:10
%S 8191,2730,1091,623,340,260,182,154,121,94,89,74,66,62,55,48,43,39,35,
%T 31,28,25,23,19,15,12,11,9,7,5,1
%N a(n)=number of numbers removed in each step of Eratosthenes's sieve for 2^14.
%C Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
%C Number of primes less than 2^14 is equal to 2^14 - (sum all of numbers in this sequence) - 1 = A007053(14).
%t f3[k_Integer?Positive, i_Integer?Positive] := Module[{f, m, r, p}, p = Transpose[{r = Range[2, i], Prime[r]}];f[x_] := Catch[Fold[If[Mod[x, #2[[2]]] == 0, Throw[m[ #2[[1]]] = m[ #2[[1]]] + 1], #1] &, If[Mod[x, 2] == 0, Throw[m[1] = m[1] + 1]], p]]; Table[m[n] = -1, {n, i}]; f /@ Range[k]; Table[m[n], {n, i}]];nn = 14; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
%Y Cf. A006880, A122121, A145532-A145540, A145583-A145592.
%K fini,full,nonn
%O 1,1
%A _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008
|