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A145537 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 10!. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 14:46 EDT 2021. Contains 343089 sequences. (Running on oeis4.)