OFFSET
1,3
COMMENTS
Equivalently, n divided by the largest factorial divisor of n.
Also, the smallest r such that n/r is a factorial number.
Positions of 1's are the factorial numbers A000142. Is every positive integer in this sequence? - Gus Wiseman, May 15 2019
Let m = A055874(n), the largest integer such that 1,2,...,m divides n. Then a(n*m!) = n since m+1 does not divide n, showing that every integer is part of the sequence. - Etienne Dupuis, Sep 19 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
FORMULA
From Amiram Eldar, Dec 25 2023: (Start)
a(n) = n/A055881(n)!.
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = BesselI(2, 2) = 0.688948... (A229020). (End)
MATHEMATICA
Table[n/Max@@Intersection[Divisors[n], Array[Factorial, n]], {n, 100}] (* Gus Wiseman, May 15 2019 *)
a[n_] := Module[{k=1}, While[Divisible[n, k!], k++]; n/(k-1)!]; Array[a, 100] (* Amiram Eldar, Dec 25 2023 *)
PROG
(PARI) first(n) = {my(res = [1..n]); for(i = 2, oo, k = i!; if(k <= n, for(j = 1, n\k, res[j*k] = j ) , return(res) ) ) } \\ David A. Corneth, Sep 19 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Oct 19 2002
EXTENSIONS
More terms from David A. Corneth, Sep 19 2020
STATUS
approved