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Number of 11-almost primes less than or equal to 10^n.
9

%I #6 Jul 06 2012 11:49:58

%S 0,0,0,0,7,138,1878,23448,279286,3230577,36585097,407818620,

%T 4490844534,48972151631,529781669333

%N Number of 11-almost primes less than or equal to 10^n.

%e There are 7 eleven-almost primes up to 10000: 2048, 3072, 4608, 5120, 6912, 7168 & 7680.

%t 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, 10^n], {n, 12}]

%Y Cf. A066265, A014613, A116382.

%Y Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.

%K nonn

%O 0,5

%A _Robert G. Wilson v_, Feb 07 2006

%E a(14) from _Robert G. Wilson v_, Jan 07 2007