This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116429 #11 Aug 05 2023 22:00:05
%S A116429 1,4,26,181,1095,6416,35285,187929,973404,4934952,24628655,121375817,
%T A116429 592337729,2868086641,13798982719,66043675287,314715355786,
%U A116429 1494166794434,7071357084444,33374079939405
%N A116429 The number of n-almost primes less than or equal to 9^n, starting with a(0)=1.
%t A116429 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 A116429 Table[ AlmostPrimePi[n, 9^n], {n, 13}]
%o A116429 (PARI)
%o A116429 almost_prime_count(N, k) = if(k==1, return(primepi(N))); (f(m, p, k, j=0) = my(c=0, s=sqrtnint(N\m, k)); if(k==2, forprime(q=p, s, c += primepi(N\(m*q))-j; j += 1), forprime(q=p, s, c += f(m*q, q, k-1, j); j += 1)); c); f(1, 2, k);
%o A116429 a(n) = if(n == 0, 1, almost_prime_count(9^n, n)); \\ _Daniel Suteu_, Jul 10 2023
%Y A116429 Cf. A078840, A078841, A078842, A116432, A078843, A116426, A078844, A116427, A078845, A116428, A116429, A116430, A078846, A116431.
%K A116429 nonn,more
%O A116429 0,2
%A A116429 _Robert G. Wilson v_, Feb 10 2006
%E A116429 a(14)-a(16) from _Donovan Johnson_, Oct 01 2010
%E A116429 a(16) corrected and a(17)-a(19) from _Daniel Suteu_, Jul 10 2023