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

181439, 60479, 24191, 13823, 7540, 5800, 4092, 3446, 2701, 2046, 1842, 1487, 1296, 1200, 1070, 927, 817, 782, 703, 665, 645, 600, 574, 538, 498, 477, 465, 451, 441, 425, 385, 372, 351, 346, 326, 322, 308, 294, 288, 277, 267, 263, 248, 246, 238, 236, 221, 211

Offset

1,1

Comments

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

Number of primes less than 9! is 9! - (sum all numbers in this sequence) - 1 = A003604(9).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..110 (full sequence)

Maple

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

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 = 9; kk = PrimePi[Sqrt[nn! ]]; t3 = f3[nn!, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

Crossrefs

Cf. A003604, A133228, A145532-A145540.

Sequence in context: A274365 A209828 A133541 * A375118 A249959 A250013

Adjacent sequences: A145533 A145534 A145535 * A145537 A145538 A145539

Keyword

fini,nonn

Author

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

Status

approved