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 A116426 #14 Oct 02 2024 12:29:48
%S A116426 1,2,6,13,34,77,177,406,887,1962,4225,9094,19482,41414,87706,184976,
%T A116426 389357,816193,1708412,3566209,7431153,15457234,32098652,66560309,
%U A116426 137830562,285062028,588871107,1215176367,2505048537,5159228725
%N A116426 The number of n-almost primes less than or equal to 4^n, starting with a(0)=1.
%t A116426 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 A116426 Join[{1},Table[AlmostPrimePi[n, 4^n], {n, 29}]]
%o A116426 (Python)
%o A116426 from math import isqrt, prod
%o A116426 from sympy import primerange, integer_nthroot, primepi
%o A116426 def A116426(n):
%o A116426 if n<=1: return n+1
%o A116426 def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b,isqrt(x//c)+1),a)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b,integer_nthroot(x//c,m)[0]+1),a) for d in g(x,a2,b2,c*b2,m-1)))
%o A116426 return int(sum(primepi((1<<(n<<1))//prod(c[1] for c in a))-a[-1][0] for a in g(1<<(n<<1),0,1,1,n))) # _Chai Wah Wu_, Oct 02 2024
%Y A116426 Cf. A078840, A078841, A078842, A116432, A078843, A116426, A078844, A116427, A078845, A116428, A116429, A116430, A078846, A116431.
%K A116426 nonn
%O A116426 0,2
%A A116426 _Robert G. Wilson v_, Feb 10 2006