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A339919 a(n) = Sum_{k=1..n} (floor(3*n/k) - 3*floor(n/k)). 2
0, 0, 0, 1, 1, 3, 1, 5, 4, 4, 5, 9, 5, 7, 10, 10, 8, 13, 8, 16, 13, 11, 15, 19, 14, 15, 18, 21, 18, 22, 17, 23, 22, 22, 26, 30, 18, 24, 29, 31, 28, 31, 26, 32, 33, 29, 32, 42, 32, 35, 34, 36, 39, 41, 40, 42, 37, 40, 41, 53, 38, 44, 49, 47, 47, 47, 43, 53, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

LINKS

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

FORMULA

a(n) ~ (3*log(3) - 5/2) * n.

MATHEMATICA

Table[Sum[Floor[3*n/k] - 3*Floor[n/k], {k, 1, n}], {n, 0, 100}]

PROG

(PARI) a(n) = sum(k=1, n, floor(3*n/k) - 3*floor(n/k)); \\ Michel Marcus, Dec 23 2020

CROSSREFS

Cf. A006218, A059851, A075989, A339918.

Sequence in context: A068512 A011090 A260629 * A112620 A325766 A021321

Adjacent sequences:  A339916 A339917 A339918 * A339920 A339921 A339922

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 23 2020

STATUS

approved

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Last modified September 27 07:39 EDT 2021. Contains 347672 sequences. (Running on oeis4.)