A145535 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 8!.

20159, 6719, 2687, 1535, 836, 642, 454, 381, 297, 223, 204, 170, 154, 146, 134, 119, 108, 103, 92, 84, 81, 76, 70, 64, 56, 53, 51, 47, 45, 42, 36, 32, 30, 28, 23, 21, 18, 16, 15, 12, 8, 6, 5, 3, 2, 1

Offset: 1

Author

Artur Jasinski with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008

Keywords

• fini
• full
• nonn

Comments

Number of steps in Eratosthenes's sieve for n! is A133228(n).

Number of primes less than 8! is 8! - (sum all numbers in this sequence) - 1 = A003604(8).

Crossrefs

Cf. A003604, A133228, A145532-A145540.

Programs

Maple

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

Mathematica

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) *)