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%I #7 Jul 21 2015 05:02:19
%S 0,0,12,149,1712,18744,198062,2050696,20959322,212385942,2139236881,
%T 21454599814,214499908019,2139634739326,21306682904040,
%U 211905511283590,2105504493045818,20905484578206982
%N Number of 4-almost primes less than or equal to 10^n.
%e There are 12 primes with four almost primes up to 100: 16,24,36,40,54,56,60,81,84,88,90&100.
%t FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}]; Table[ FourAlmostPrimePi[n], {n, 0, 13}]
%Y Cf. A006880, A066265, A109251, A014613.
%K nonn
%O 0,3
%A _Robert G. Wilson v_, Feb 07 2006
%E a(14) from _Robert G. Wilson v_, Jan 07 2007
%E a(15)-a(17) from _Henri Lifchitz_, Jul 21 2015
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