OFFSET
0,3
FORMULA
a(n) = A072114(10^n). - R. J. Mathar, May 25 2008
EXAMPLE
There are 22 numbers with three prime factors up to 10^2: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99.
MATHEMATICA
ThreeAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j)] - j + 1, {i, PrimePi[n^(1/3)]}, {j, i, PrimePi@ Sqrt[n/Prime@i]}]; Table[ ThreeAlmostPrimePi[10^n], {n, 0, 14}] (* Robert G. Wilson v *)
PROG
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A109251(n):
r = 10**n
return int(sum(primepi(r//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(r, 3)[0]+1)) for b, m in enumerate(primerange(k, isqrt(r//k)+1), a))) # Chai Wah Wu, Sep 18 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Martin Raab, Aug 19 2005
EXTENSIONS
a(10)-a(14) from Robert G. Wilson v, Feb 06 2006
a(15)-a(17) from Hiroaki Yamanouchi, Aug 30 2014
a(18)-a(19) from Henri Lifchitz, Dec 01 2014
STATUS
approved