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

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

Author

Vaclav Kotesovec, Dec 23 2020

Keywords

• nonn

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

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

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.