A101041 Number of numbers not greater than n having no more than two prime factors.

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, 20, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 28, 29, 29, 30, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46

Offset: 1

Author

Reinhard Zumkeller, Nov 28 2004

Keywords

• nonn

Comments

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

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

Primes counted with multiplicity. - Harvey P. Dale, Feb 16 2024

Crossrefs

Cf. A000720, A072000, A101040.

Programs

Mathematica

Accumulate[Table[If[PrimeOmega[n]<3,1,0],{n,80}]] (* Harvey P. Dale, Feb 16 2024 *)

Formula

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