|
%I #14 Jul 23 2019 01:51:26
%S 0,1,1,2,1,2,1,2,3,1,3,2,1,2,4,3,1,3,2,1,4,2,3,4,2,1,2,1,2,5,2,4,1,5,
%T 1,3,4,2,6,3,1,5,1,2,1,5,6,2,1,2,3,1,6,5,4,3,1,3,2,1,7,6,2,1,2,7,3,5,
%U 1,2,3,8,4,6,2,3,7,2,6,4,1,4,1,8,2,3,5,2,1,2,5,6,2,7,2,3,5,1,9,3,8,6,3,1,3
%N a(n) = pi(A052180(n)) = A000720(A052180(n)); subscript of last prime used in Eratosthenes sieve by which all composites between n-th and (n+1)th primes were excluded.
%e Of composites between the 24th and 25th primes (89, 97), the least prime divisors are {2,7,2,3,2,5,2}.
%e The largest of these is 7. This means that pi(7)=4 steps in prime sieving are required to sweep out all composites between 89 and 97: {90,92,94,96}, (93}, {95}, and {91} were excluded in the 1st, 2nd, 3rd, and 4th steps, respectively.
%e So a(24)=4.
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] mi[x_] := Min[ba[x]] Table[PrimePi[Max[Table[mi[ba[w]], {w, Prime[j]+1, -1+Prime[j+1]}]]], {j, 1, 30}]
%Y Cf. A052180, A000720.
%K nonn
%O 1,4
%A _Labos Elemer_, May 14 2003
|
