|
%I #18 Feb 23 2019 19:47:03
%S 49999,16666,6666,3808,2077,1597,1127,949,741,555,499,405,358,335,305,
%T 274,248,242,219,203,199,184,175,165,148,141,137,131,128,124,108,104,
%U 97,95,87,86,79,75,70,67,62,60,57,54,52,50,45,39,37,35,32,29,28,25,23,20
%N Number of numbers removed in each step of Eratosthenes's sieve for 10^5.
%C Number of steps in Eratosthenes's sieve for 10^n is A122121(n).
%C Number of primes less than 10^5 equals 10^5 - A065894(5) (sum of all numbers in this sequence) - 1 = A006880(5).
%C a(n) is the number of composite numbers m <= 10^5 whose least prime factor (A020639(m)) is prime(n).
%H Nathaniel Johnston, <a href="/A145538/b145538.txt">Table of n, a(n) for n = 1..65</a> (full sequence)
%p 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
%t 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) *)
%Y Cf. A006880, A122121, A145532-A145540.
%Y Cf. A065894, A020639.
%K fini,full,nonn
%O 1,1
%A _Artur Jasinski_ with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008
%E Edited by _Rick L. Shepherd_, Mar 02 2013
|
