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Number of numbers not greater than n having no more than two prime factors.
1

%I #10 Feb 16 2024 14:47:28

%S 1,2,3,4,5,6,7,7,8,9,10,10,11,12,13,13,14,14,15,15,16,17,18,18,19,20,

%T 20,20,21,21,22,22,23,24,25,25,26,27,28,28,29,29,30,30,30,31,32,32,33,

%U 33,34,34,35,35,36,36,37,38,39,39,40,41,41,41,42,42,43,43,44,44,45,45,46

%N Number of numbers not greater than n having no more than two prime factors.

%C a(n) = 1 + Sum_{k=1..n} A101040(k);

%C asymptotically: a(n) ~ n*log(log(n))/log(n).

%C Primes counted with multiplicity. - _Harvey P. Dale_, Feb 16 2024

%F a(n) = A000720(n) + A072000(n) + 1.

%t Accumulate[Table[If[PrimeOmega[n]<3,1,0],{n,80}]] (* _Harvey P. Dale_, Feb 16 2024 *)

%Y Cf. A000720, A072000, A101040.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 28 2004