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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A339918 a(n) = Sum_{k=1..n} floor(3*n/k).

Original entry on oeis.org

0, 3, 9, 16, 25, 33, 43, 53, 64, 73, 86, 96, 110, 118, 133, 145, 158, 169, 182, 196, 211, 221, 237, 247, 266, 276, 291, 306, 321, 331, 350, 362, 379, 391, 407, 423, 438, 450, 467, 481, 502, 511, 530, 542, 561, 575, 590, 606, 626, 638, 655, 669, 690, 698, 721
Offset: 0

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Author

Vaclav Kotesovec, Dec 23 2020

Keywords

Comments

In general, for m>=1, Sum_{k=1..n} floor(m*n/k) ~ m*n * (log(m*n) + 2*gamma - H(m)), where H(m) = A001008(m)/A002805(m) is the m-th harmonic number and gamma is the Euler-Mascheroni constant A001620.

Links

Crossrefs

Cf. A006218, A339217, A339919.

Programs

  • Mathematica
    Table[Sum[Floor[3*n/k], {k, 1, n}], {n, 0, 100}]
  • PARI
    a(n) = sum(k=1, n, floor(3*n/k)); \\ Michel Marcus, Dec 23 2020

Formula

a(n) ~ 3*n * (log(3*n) + 2*gamma - 11/6), where gamma is the Euler-Mascheroni constant A001620.
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