A145533 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 6!.

359, 119, 47, 26, 14, 11, 7, 5, 3

Offset: 1

Author

Artur Jasinski, Oct 12 2008

Keywords

• fini
• full
• nonn

Comments

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

Number of primes less than 6! is 720 - 359 - 119 - 47 - 26 - 14 - 11 - 7 - 5 - 3 - 1 = 128 = A003604(6).

Examples

			a(1)=359 because in the first step we remove all numbers divisible by 2 (= 360) with the exception of the first one, i.e., 2.
a(2)=119 because the number of numbers divisible by 3 and not divisible by 2 is 120 and we remove all such numbers with the exception of the first one, 3.
		

Crossrefs

Cf. A003604, A133228, A145532-A145540.

Programs

Maple

A145533 := {$(1..6!)}: for n from 1 do p:=ithprime(n): r:=0: lim:=6!/p: for k from 2 to lim do if(member(k*p,A145533))then r:=r+1: fi: A145533 := A145533 minus {k*p}: od: printf("%d, ", r): if(r=0)then break: fi: od: # Nathaniel Johnston, Jun 23 2011

Mathematica

{m1, m2, m3, m4, m5, m6, m7, m8, m9} = {-1, -1, -1, -1, -1, -1, -1, -1, -1};
Do[If[Mod[n, 2] == 0, m1 = m1 + 1,
If[Mod[n, 3] == 0, m2 = m2 + 1,
If[Mod[n, 5] == 0, m3 = m3 + 1,
If[Mod[n, 7] == 0, m4 = m4 + 1,
If[Mod[n, 11] == 0, m5 = m5 + 1,
If[Mod[n, 13] == 0, m6 = m6 + 1,
If[Mod[n, 17] == 0, m7 = m7 + 1,
If[Mod[n, 19] == 0, m8 = m8 + 1,
If[Mod[n, 23] == 0, m9 = m9 + 1]]]]]]]]], {n, 1, 6!}];
Print[{m1, m2, m3, m4, m5, m6, m7, m8, m9}] (* Artur Jasinski *)