A145538 Number of numbers removed in each step of Eratosthenes's sieve for 10^5.

49999, 16666, 6666, 3808, 2077, 1597, 1127, 949, 741, 555, 499, 405, 358, 335, 305, 274, 248, 242, 219, 203, 199, 184, 175, 165, 148, 141, 137, 131, 128, 124, 108, 104, 97, 95, 87, 86, 79, 75, 70, 67, 62, 60, 57, 54, 52, 50, 45, 39, 37, 35, 32, 29, 28, 25, 23, 20

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 10^n is A122121(n).

Number of primes less than 10^5 equals 10^5 - A065894(5) (sum of all numbers in this sequence) - 1 = A006880(5).

a(n) is the number of composite numbers m <= 10^5 whose least prime factor (A020639(m)) is prime(n).

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..65 (full sequence)

Crossrefs

Cf. A006880, A122121, A145532-A145540.

Cf. A065894, A020639.

Programs

Maple

A145538:=Array([seq(0,j=1..65)]): lim:=10^5: p:=Array([seq(ithprime(j),j=1..65)]): for n from 4 to lim do if(isprime(n))then n:=n+1: fi: for k from 1 to 65 do if(n mod p[k] = 0)then A145538[k]:=A145538[k]+1: break: fi: od: od: seq(A145538[j],j=1..65); # 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 = 5; kk = PrimePi[Sqrt[10^nn]]; t3 = f3[10^nn, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

Extensions

Edited by Rick L. Shepherd, Mar 02 2013