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

4, 34, 299, 2625, 23378, 210035, 1904324, 17427258, 160788536, 1493776443, 13959990342, 131126017178, 1237088048653, 11715902308080, 111329817298881, 1061057292827269, 10139482913717352, 97123037685177087, 932300026230174178, 8966605849641219022, 86389956293761485464, 833671466551239927908, 8056846659984852885191

Offset: 1

Author

Shyam Sunder Gupta

Keywords

• nonn

Links

• Dragos Krisan and Radek Erban, On the counting function of semiprimes, arXiv:2006.16491 [math.NT], 8 Jul 2020.

Crossrefs

Essentially the same as A066265.

Programs

Mathematica

SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] - i + 1, {i, PrimePi@ Sqrt@ n}]; Array[ SemiPrimePi[10^#] &, 14] (* Robert G. Wilson v, Feb 12 2015 *)

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

Python

from math import isqrt
from sympy import primepi, primerange
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

Extensions

a(14) from Robert G. Wilson v, May 16 2005

a(15)-a(16) from Donovan Johnson, Mar 18 2010

a(17)-a(18) from A066265, added by Jens Kruse Andersen, Aug 16 2014

a(19)-a(21) from Henri Lifchitz, Jul 04 2015

a(22)-a(23) from Henri Lifchitz, Nov 09 2024