A140234 Sum of the semiprimes <= n.

0, 0, 0, 0, 4, 4, 10, 10, 10, 19, 29, 29, 29, 29, 43, 58, 58, 58, 58, 58, 58, 79, 101, 101, 101, 126, 152, 152, 152, 152, 152, 152, 152, 185, 219, 254, 254, 254, 292, 331, 331, 331, 331, 331, 331, 331, 377, 377, 377, 426, 426, 477, 477, 477, 477, 532, 532, 589

Offset: 0

Author

Jonathan Vos Post, May 13 2008

Keywords

• easy
• nonn

Comments

This is to semiprimes A001358 as A034387 is to primes A000040. From the prime number theorem A034387(n) has the asymptotic expression: a(n) ~ n^2 / (2 log n), so what is the asymptotic expression for a(n)?

Crossrefs

Cf. A001358, A034387, A051352, A062198, A072000, A100959, A140235.

Programs

Mathematica

a[n_]:=Total[Select[Range[n],PrimeOmega[#]==2&]];Array[a,58,0] (* James C. McMahon, Jul 06 2025 *)

Formula

a(n) = Sum_{j such that j is in A001358 and j<=n} = A062198(A072000(n)).