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A076934
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Smallest integer of the form n/k!.
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19
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1, 1, 3, 2, 5, 1, 7, 4, 9, 5, 11, 2, 13, 7, 15, 8, 17, 3, 19, 10, 21, 11, 23, 1, 25, 13, 27, 14, 29, 5, 31, 16, 33, 17, 35, 6, 37, 19, 39, 20, 41, 7, 43, 22, 45, 23, 47, 2, 49, 25, 51, 26, 53, 9, 55, 28, 57, 29, 59, 10, 61, 31, 63, 32, 65, 11, 67, 34, 69, 35, 71
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = BesselI(2, 2) = 0.688948... (A229020). (End)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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