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 A120051 #21 Mar 20 2025 06:00:14
%S A120051 0,0,0,0,22,306,4016,49163,578154,6618221,74342563,823164388,
%T A120051 9011965866,97765974368,1052666075366,11263041623194,119864659464824,
%U A120051 1269754732725522,13396817167474205,140847445420555406
%N A120051 Number of 10-almost primes less than or equal to 10^n.
%e A120051 There are 22 ten-almost primes up to 10000: 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, and 9984.
%t A120051 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 A120051 Table[AlmostPrimePi[10, 10^n], {n, 12}]
%o A120051 (Python)
%o A120051 from math import isqrt, prod
%o A120051 from sympy import primerange, integer_nthroot, primepi
%o A120051 def A120051(n):
%o A120051 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 A120051 return int(sum(primepi(10**n//prod(c[1] for c in a))-a[-1][0] for a in g(10**n,0,1,1,10))) # _Chai Wah Wu_, Nov 03 2024
%Y A120051 Cf. A066265, A014613, A116382.
%Y A120051 Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.
%K A120051 nonn,more
%O A120051 0,5
%A A120051 _Robert G. Wilson v_, Feb 07 2006
%E A120051 More terms from _Robert G. Wilson v_, Jan 07 2007
%E A120051 a(15)-a(19) from _Henri Lifchitz_, Mar 20 2025