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A145584 a(n) = number of numbers removed in step n of Eratosthenes's sieve for 2^6.

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%I A145584 #25 Sep 14 2023 18:07:42
%S A145584 31,10,3,1
%N A145584 a(n) = number of numbers removed in step n of Eratosthenes's sieve for 2^6.
%C A145584 Number of steps in Eratosthenes's sieve for 2^n is A060967(n).
%C A145584 Number of primes less than 2^6 is equal to 2^6 - (sum all of numbers in this sequence) - 1 = A007053(6).
%t A145584 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 = 6; kk = PrimePi[Sqrt[2^nn]]; t3 = f3[2^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
%Y A145584 Cf. A006880, A122121.
%Y A145584 Cf. A145532, A145533, A145534, A145535, A145536, A145537, A145538, A145539, A145540.
%Y A145584 Cf. A145583, A145584, A145585, A145586, A145587, A145588, A145589, A145590, A145591, A145592.
%K A145584 fini,full,nonn
%O A145584 1,1
%A A145584 _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008