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 A036352 #33 Dec 17 2024 12:56:19 %S A036352 4,34,299,2625,23378,210035,1904324,17427258,160788536,1493776443, %T A036352 13959990342,131126017178,1237088048653,11715902308080, %U A036352 111329817298881,1061057292827269,10139482913717352,97123037685177087,932300026230174178,8966605849641219022,86389956293761485464,833671466551239927908,8056846659984852885191 %N A036352 Number of numbers up to 10^n that are products of two primes. %H A036352 Dragos Krisan and Radek Erban, <a href="https://arxiv.org/abs/2006.16491">On the counting function of semiprimes</a>, arXiv:2006.16491 [math.NT], 8 Jul 2020. %t A036352 SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] - i + 1, {i, PrimePi@ Sqrt@ n}]; Array[ SemiPrimePi[10^#] &, 14] (* _Robert G. Wilson v_, Feb 12 2015 *) %o A036352 (PARI) a(n)=my(s);forprime(p=2,sqrt(10^n),s+=primepi(10^n\p)); s-binomial(primepi(sqrt(10^n)),2) \\ _Charles R Greathouse IV_, Apr 23 2012 %o A036352 (Python) %o A036352 from math import isqrt %o A036352 from sympy import primepi, primerange %o A036352 def A036352(n): return int((-(t:=primepi(s:=isqrt(m:=10**n)))*(t-1)>>1)+sum(primepi(m//k) for k in primerange(1, s+1))) # _Chai Wah Wu_, Aug 16 2024 %Y A036352 Essentially the same as A066265. %K A036352 nonn %O A036352 1,1 %A A036352 _Shyam Sunder Gupta_ %E A036352 a(14) from _Robert G. Wilson v_, May 16 2005 %E A036352 a(15)-a(16) from _Donovan Johnson_, Mar 18 2010 %E A036352 a(17)-a(18) from A066265, added by _Jens Kruse Andersen_, Aug 16 2014 %E A036352 a(19)-a(21) from _Henri Lifchitz_, Jul 04 2015 %E A036352 a(22)-a(23) from _Henri Lifchitz_, Nov 09 2024