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

1,2

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

Links

Table of n, a(n) for n=1..73.

Formula

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

Mathematica

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

Crossrefs

Cf. A000720, A072000, A101040.

Sequence in context: A271490 A252649 A095703 * A093697 A157466 A194260

Adjacent sequences: A101038 A101039 A101040 * A101042 A101043 A101044

Keyword

nonn

Author

Reinhard Zumkeller, Nov 28 2004

Status

approved