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%I #15 Sep 08 2023 22:49:14
%S 4095,1364,545,311,170,130,91,77,63,51,46,36,34,29,26,21,17,15,12,11,
%T 9,6,3,1
%N a(n)=number of numbers removed in each step of Eratosthenes's sieve for 2^13.
%C Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
%C Number of primes less than 2^13 is equal to 2^13 - (sum all of numbers in this sequence) - 1 = A007053(13).
%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 = 13; 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,nonn
%O 1,1
%A _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008