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A145536 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 9!.

%I A145536 #13 Feb 23 2019 19:46:37
%S A145536 181439,60479,24191,13823,7540,5800,4092,3446,2701,2046,1842,1487,
%T A145536 1296,1200,1070,927,817,782,703,665,645,600,574,538,498,477,465,451,
%U A145536 441,425,385,372,351,346,326,322,308,294,288,277,267,263,248,246,238,236,221,211
%N A145536 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 9!.
%C A145536 Number of steps in Eratosthenes's sieve for n! is A133228(n).
%C A145536 Number of primes less than 9! is 9! - (sum all numbers in this sequence) - 1 = A003604(9).
%H A145536 Nathaniel Johnston, <a href="/A145536/b145536.txt">Table of n, a(n) for n = 1..110</a> (full sequence)
%p A145536 A145536:=Array([seq(0,j=1..110)]): lim:=9!: p:=Array([seq(ithprime(j),j=1..110)]): for n from 4 to lim do if(isprime(n))then n:=n+1: fi: for k from 1 to 110 do if(n mod p[k] = 0)then A145536[k]:=A145536[k]+1: break: fi: od: od: seq(A145536[j],j=1..110); # _Nathaniel Johnston_, Jun 23 2011
%t A145536 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 = 9; kk = PrimePi[Sqrt[nn! ]]; t3 = f3[nn!, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)
%Y A145536 Cf. A003604, A133228, A145532-A145540.
%K A145536 fini,nonn
%O A145536 1,1
%A A145536 _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008