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A345683 a(n) = n! * Sum_{k=1..n} 1/floor(n/k). 5
1, 3, 14, 66, 444, 2880, 25080, 216720, 2247840, 24071040, 304335360, 3752179200, 54965433600, 810550540800, 13176376012800, 219079045785600, 4078723532083200, 75227891042304000, 1550619342784512000, 31871016307113984000, 710529031487987712000, 16180987966182014976000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..448

Vaclav Kotesovec, Plot a(n) / (n*n!) for n = 1..1000000

Mathoverflow, An asymptotic formula for a sum involving powers of floor functions, 2019.

FORMULA

a(n) ~ c * n * n!, where c = Sum_{j>=1} 1/(j^2*(j+1)) = Pi^2/6 - 1 = 0.644934... [proved by Harry Richman, see Mathoverflow link]

MATHEMATICA

Table[n! * Sum[1/Floor[n/k], {k, 1, n}], {n, 1, 25}]

Table[n!*(Sum[(Floor[n/j] - Floor[n/(j + 1)])/j, {j, 1, n}]), {n, 1, 25}]

PROG

(PARI) a(n) = n!*sum(k=1, n, 1/(n\k)); \\ Michel Marcus, Jun 24 2021

CROSSREFS

Cf. A006218, A010786, A092143, A117871, A345682, A345684, A345686.

Sequence in context: A034275 A240008 A151322 * A002320 A151323 A181662

Adjacent sequences:  A345680 A345681 A345682 * A345684 A345685 A345686

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 23 2021

STATUS

approved

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Last modified September 20 21:32 EDT 2021. Contains 347591 sequences. (Running on oeis4.)