cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A140234 Sum of the semiprimes <= n.

Original entry on oeis.org

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

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Author

Jonathan Vos Post, May 13 2008

Keywords

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)).
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