A292785 Number of odd squarefree semiprimes < 10^n.

0, 16, 194, 1932, 18181, 168330, 1555366, 14424896, 134429269, 1258812629, 11840308472, 111817802539, 1059796159358, 10076977878935, 96091981692305, 918679869869451, 8803388128870716, 84537081067757934, 813340036390023775, 7838825925395981969, 75669246174605279757

Offset: 1

Author

Hugo Pfoertner, Oct 10 2017

Keywords

• nonn

Examples

			a(2)=16 because there are 16 squarefree odd semiprimes < 10^2: 15=3*5, 21=3*7, 33=3*11, 35=5*7, 39=3*13, 51=3*17, 55=5*11, 57=3*19, 65=5*13, 69=3*23, 77=7*11, 85=5*17, 87=3*29, 91=7*13, 93=3*31, 95=5*19.
		

Crossrefs

Cf. A046388, A066265, A122121, A220262.

Programs

Mathematica

-1 + Accumulate@ Table[Count[Range[10^n + 1, 10^(n + 1) - 1, 2], ?(And[ SquareFreeQ@ #, PrimeNu[#] == 2] &)], {n, 0, 5}] (* _Michael De Vlieger, Oct 10 2017 *)

Python

from math import isqrt
from sympy import primepi, primerange
def A292785(n): return int((-(t:=primepi(s:=isqrt(m:=10**n)))*(t+1)>>1)+1+sum(primepi(m//k) for k in primerange(3, s+1))) if n>1 else 0 # Chai Wah Wu, Oct 17 2024

Formula

a(n) = A066265(n) - A122121(n) - A220262(n) + 1 for n > 1.

Extensions

a(21) from Jinyuan Wang, Jul 30 2021