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 A010786 Floor-factorial numbers: a(n) = Product_{k=1..n} floor(n/k). 18
 1, 2, 3, 8, 10, 36, 42, 128, 216, 600, 660, 3456, 3744, 9408, 18900, 61440, 65280, 279936, 295488, 1152000, 2116800, 4878720, 5100480, 31850496, 41472000, 93450240, 163762560, 568995840, 589317120, 3265920000, 3374784000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Product floor(n/1)*floor(n/2)*floor(n/3)*...*floor(n/n). a(n) is the number of functions f:[n]->[n] where f(x) is a multiple of x for all x in [n]. We note that there are floor[n/x] possible choices for each image of x under f. [Dennis P. Walsh, Nov 06 2014] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Vaclav Kotesovec, Graph - The asymptotic ratio (1000000 terms) Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant FORMULA a(n+1) = a(n)*A208449(n)/A208450(n). - Reinhard Zumkeller, Feb 26 2012 GCD(a(n), a(n+1)) = A208448(n). - Reinhard Zumkeller, Feb 26 2012 From Vaclav Kotesovec, Oct 03 2018: (Start) log(a(n)) ~ c * (n - log(2*Pi*n)/2), where c = 0.7885... Conjecture: c = A085361. (End) EXAMPLE For n=4 the a(4)=8 functions are given by the image sequences <1,2,3,4>, <1,4,3,4>, <2,2,3,4>, <2,4,3,4>, <3,2,3,4>, <3,4,3,4>, <4,2,3,4>, and <4,4,3,4>. [Dennis P. Walsh, Nov 06 2014] MAPLE a := n -> mul( floor(n/k), k=1..n); MATHEMATICA Table[Product[Floor[n/k], {k, n}], {n, 40}] (* Harvey P. Dale, May 09 2017 *) PROG (Haskell) a010786 n = product \$ map (div n) [1..n] -- Reinhard Zumkeller, Feb 26 2012 (PARI) vector(50, n, prod(k=1, n, n\k)) \\ Michel Marcus, Nov 10 2014 (MAGMA) [&*[n div i: i in [1..n]]: n in [1..35]]; // Vincenzo Librandi, Oct 03 2018 CROSSREFS Cf. A006218, A075885, A131385, A131387. Sequence in context: A165153 A121989 A320843 * A248822 A005727 A118089 Adjacent sequences:  A010783 A010784 A010785 * A010787 A010788 A010789 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Hieronymus Fischer, Jul 08 2007 Edited by N. J. A. Sloane, Jul 05 2008 at the suggestion of Rick L. Shepherd STATUS approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)