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A145535 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 8!. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

LINKS

Table of n, a(n) for n=1..46.

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) *)

CROSSREFS

Cf. A003604, A133228, A145532-A145540.

Sequence in context: A186565 A186480 A204864 * A190474 A109479 A003808

Adjacent sequences:  A145532 A145533 A145534 * A145536 A145537 A145538

KEYWORD

fini,full,nonn

AUTHOR

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

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)