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 A120053 #24 Mar 20 2025 06:00:30
%S A120053 0,0,0,0,3,63,865,11068,133862,1563465,17836903,200051717,2214357712,
%T A120053 24255601105,263439785143,2841076717752,30457549169277,
%U A120053 324855769153426,3449587218984911,36489283363168885
%N A120053 Number of 12-almost primes less than or equal to 10^n.
%e A120053 There are 3 twelve-almost primes up to 10000: 4096, 6144, and 9216.
%t A120053 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 A120053 Table[AlmostPrimePi[12, 10^n], {n, 11}]
%o A120053 (Python)
%o A120053 from math import prod, isqrt
%o A120053 from sympy import primerange, integer_nthroot, primepi
%o A120053 def A120053(n):
%o A120053 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 A120053 return int(sum(primepi(10**n//prod(c[1] for c in a))-a[-1][0] for a in g(10**n,0,1,1,12))) # _Chai Wah Wu_, Aug 23 2024
%Y A120053 Cf. A066265, A014613, A116382.
%Y A120053 Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.
%K A120053 nonn,more
%O A120053 0,5
%A A120053 _Robert G. Wilson v_, Feb 07 2006
%E A120053 a(13) and a(14) from _Robert G. Wilson v_, Jan 07 2007
%E A120053 a(15) from _Chai Wah Wu_, Aug 24 2024
%E A120053 a(16)-a(19) from _Henri Lifchitz_, Mar 18 2025