OFFSET
0,13
COMMENTS
The partial sum equals the number of Pi_11(2^n).
EXAMPLE
(2^11, 2^12] there is one semiprime, namely 3072. 2048 was counted in the previous entry.
MATHEMATICA
AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]]; (* Eric W. Weisstein, Feb 07 2006 *)
t = Table[AlmostPrimePi[11, 2^n], {n, 0, 30}]; Rest@t - Most@t
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post and Robert G. Wilson v, Mar 21 2006
STATUS
approved