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%I #4 Mar 31 2012 20:01:54
%S 1,1,2,4,5,7,12,18,24,37,54,74,107,159,218,315,450,634,888,1269,1782,
%T 2496,3520,4933,6899,9681,13555,18888,26407,36855,51352,71526,99654,
%U 138608,192708,267833,372107,516420,716816,994191,1378195,1909694
%N The number of n-almost primes less than or equal to e^n, starting with a(0)=1.
%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[n, E^n], {n, 42}]
%Y Cf. A078840, A078841, A078842, A116432, A078843, A116426, A078844, A116427, A078845, A116428, A116429, A116430, A078846, A116431.
%K nonn
%O 0,3
%A _Robert G. Wilson v_, Feb 10 2006
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