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

Author

Hal M. Switkay, Jan 11 2024

Keywords

• nonn
• easy

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A003418, A051451, A027750, A055874.

Programs

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 *)

PARI

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

Formula

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