A368777 a(n) is the largest divisor of n that is a term of the sequence A003418, the least common multiple of the first k natural numbers.

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 60, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 12

Offset

1,2

Comments

The graph of this sequence gives it the appearance of a ruler-like function. If n is odd, a(n) = 1. If n is even and not a multiple of 6, a(n) = 2. If n is a multiple of 6 but not of 12, a(n) = 6, and so on.

Links

Hal M. Switkay, Table of n, a(n) for n = 1..5040

Formula

a(n) = A003418(A055874(n))

Example

a(18) = 6 as 18 is divisible by lcm(1, 2, 3) = 6 but not by lcm(1, 2, 3, 4) = 12. so 6 is the largest divisor of 18 that is a term of A003418. - David A. Corneth, Jan 28 2024

Mathematica

seq[max_] := Module[{lcms = Table[LCM @@ Range[k], {k, max}]}, Table[Max[Select[Divisors[k], MemberQ[lcms, #] &]], {k, 1, max}]]; seq[100] (* Amiram Eldar, Jan 12 2024 *)

Prog

(PARI) a(n) = for(i = 2, n, if(n%i != 0, return(lcm([1..i-1])))); n \\ David A. Corneth, Jan 27 2024

Crossrefs

Cf. A003418, A051451, A027750, A055874.

Sequence in context: A053589 A055770 A225821 * A113766 A204992 A186726

Adjacent sequences: A368774 A368775 A368776 * A368778 A368779 A368780

Keyword

nonn,easy

Author

Hal M. Switkay, Jan 11 2024

Status

approved