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 A215218 #26 Aug 26 2024 13:32:21 %S A215218 0,5,135,1800,19919,206964,2086746,20710806,203834084,1997171674, %T A215218 19522428788,190614467420,1860310801454,18155356377267, %U A215218 177224592578839,1730651760050923,16908343191198752,165279853754232019,1616504757072680964 %N A215218 Number of sphenic numbers, i.e., numbers with exactly three distinct prime factors, up to 10^n. %H A215218 Paul Kinlaw, <a href="https://www.researchgate.net/publication/330506122_LOWER_BOUNDS_FOR_NUMBERS_WITH_THREE_PRIME_FACTORS">Lower bounds for numbers with three prime factors</a>, Husson University, Bangor, ME, 2019. Also in <a href="http://math.colgate.edu/~integers/t22/t22.Abstract.html">Integers</a> (2019) 19, Article #A22. %e A215218 a(2) = 5 since there are the five sphenic numbers 30, 42, 66, 70, 78 up to 100. %t A215218 f[n_] := Sum[ PrimePi[n/(Prime@ i*Prime@ j)] - j, {i, PrimePi[n^(1/3)]}, {j, i +1, PrimePi@ Sqrt[n/Prime@ i]}]; (* _Robert G. Wilson v_, Dec 28 2016 *) %o A215218 (Python) %o A215218 from math import isqrt %o A215218 from sympy import primepi, primerange, integer_nthroot %o A215218 def A215218(n): return int(sum(primepi(10**n//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(10**n,3)[0]+1),1) for b,m in enumerate(primerange(k+1,isqrt(10**n//k)+1),a+1))) # _Chai Wah Wu_, Aug 26 2024 %Y A215218 Cf. A007304. %K A215218 nonn %O A215218 1,2 %A A215218 _Martin Renner_, Aug 06 2012 %E A215218 a(8)-a(19) from _Henri Lifchitz_, Nov 11 2012