cp's OEIS Frontend

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.

A036352 Number of numbers up to 10^n that are products of two primes.

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%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