A145537 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 10!.

1814399, 604799, 241919, 138239, 75402, 58003, 40941, 34478, 26982, 20473, 18496, 15008, 13184, 12266, 10957, 9492, 8342, 7920, 7057, 6538, 6248, 5667, 5317, 4874, 4414, 4181, 4057, 3866, 3752, 3582, 3166, 3054, 2911, 2856, 2675, 2640, 2544, 2455, 2399

Offset

1,1

Comments

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

Number of primes less than 10! is 10! - (sum all numbers in this sequence) - 1 = A003604(10).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..291 (full sequence)

Maple

A145537:=Array([seq(0, j=1..291)]): lim:=10!: p:=Array([seq(ithprime(j), j=1..291)]): for n from 4 to lim do if(isprime(n))then n:=n+1: fi: for k from 1 to 291 do if(n mod p[k] = 0)then A145537[k]:=A145537[k]+1: break: fi: od: od: seq(A145537[j], j=1..291); # 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 = 10; kk = PrimePi[Sqrt[nn! ]]; t3 = f3[nn!, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

Crossrefs

Cf. A003604, A133228, A145532-A145540.

Sequence in context: A234866 A249196 A137819 * A183735 A147525 A205412

Adjacent sequences: A145534 A145535 A145536 * A145538 A145539 A145540

Keyword

fini,nonn

Author

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

Status

approved