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%I #13 Feb 23 2019 19:44:57
%S 20159,6719,2687,1535,836,642,454,381,297,223,204,170,154,146,134,119,
%T 108,103,92,84,81,76,70,64,56,53,51,47,45,42,36,32,30,28,23,21,18,16,
%U 15,12,8,6,5,3,2,1
%N a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 8!.
%C Number of steps in Eratosthenes's sieve for n! is A133228(n).
%C Number of primes less than 8! is 8! - (sum all numbers in this sequence) - 1 = A003604(8).
%p A145535 := {$(1..8!)}: for n from 1 do p:=ithprime(n): r:=0: lim:=8!/p: for k from 2 to lim do if(member(k*p,A145535))then r:=r+1: fi: A145535 := A145535 minus {k*p}: od: printf("%d, ", r): if(r=0)then break: fi: od: # _Nathaniel Johnston_, Jun 23 2011
%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 = 8; kk = PrimePi[Sqrt[nn! ]]; t3 = f3[nn!, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
%Y Cf. A003604, A133228, A145532-A145540.
%K fini,full,nonn
%O 1,1
%A _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008
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