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

1,1

Links

Table of n, a(n) for n=1..23.

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

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 *)

Prog

(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

Crossrefs

Essentially the same as A066265.

Sequence in context: A155628 A346936 A356286 * A005569 A370171 A232910

Adjacent sequences: A036349 A036350 A036351 * A036353 A036354 A036355

Keyword

nonn,changed

Author

Shyam Sunder Gupta

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

Status

approved