OFFSET
1,3
COMMENTS
Sketch of proof that a(n) is an integer from Paul R. Pudaite, 9/28/2002: 1. n! = Product{p^([n/p]+[n/p^2]+...): prime p <= n}. 2. Product{[n/k]: k = 1...n} = Product{i^([n/i]-[n/i+1]): i=2...n}. 3. = Product{Product{Product{p^([n/i]-[n/i+1]): i such that p^k|i}: k such that p^k <= n}: prime p <= n}. 4. Reorganizing the exponents in the innermost product: ([n/p^k] - [n/(p^k+1)]) + ([n/(2 p^k)] - [n/(2 p^k + 1)] + ... = [n/p^k] - ([n/(p^k+1)] - [n/(2 p^k)]) - ... <= [n/p^k].
FORMULA
a(n) = n!/A010786(n).
EXAMPLE
a(6) = 6*5*4*3*2*1/([6/1]*[6/2]*[6/3]*[6/4]*[6/5]*[6/6]) = 6!/(6*3*2*1*1*1) = 20, where [x] denotes the greatest integer <= x.
MATHEMATICA
Table[Product[k/Floor[n/k], {k, n}], {n, 30}] (* Harvey P. Dale, Feb 27 2013 *)
PROG
(PARI) a(n) = prod(k=1, n, k/(n\k)); \\ Michel Marcus, Jun 24 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 29 2002
STATUS
approved