A096179 Triangle read by rows: T(n,k) is the smallest positive integer having at least k of the first n positive integers as divisors.

1, 1, 2, 1, 2, 6, 1, 2, 4, 12, 1, 2, 4, 12, 60, 1, 2, 4, 6, 12, 60, 1, 2, 4, 6, 12, 60, 420, 1, 2, 4, 6, 12, 24, 120, 840, 1, 2, 4, 6, 12, 24, 72, 360, 2520, 1, 2, 4, 6, 12, 24, 60, 120, 360, 2520, 1, 2, 4, 6, 12, 24, 60, 120, 360, 2520, 27720, 1, 2, 4, 6, 12, 12, 24, 60, 120, 360

Offset

1,3

Links

Table of n, a(n) for n=1..76.

Wikipedia, Table of divisors.

Formula

T(n,k) = min { lcm(x_1,...,x_k) ; 0 < x_1 < ... < x_k <= n }

Example

Triangle begins:
1
1 2
1 2 6
1 2 4 12
1 2 4 12 60
1 2 4  6 12 60

Maple

with(combstruct):
a096179_row := proc(n) local k, L, l, R, LCM, comb;
R := NULL; LCM := ilcm(seq(i, i=[$1..n]));
for k from 1 to n-1 do
   L := LCM;
   comb := iterstructs(Combination(n), size=k):
   while not finished(comb) do
      l := nextstruct(comb);
      L := min(L, ilcm(op(l)));
   od;
   R := R, L;
od;
R, LCM end; # Peter Luschny, Dec 06 2010

Mathematica

(* Triangular *)
A096179[n_, k_]:=Min[LCM@@@Subsets[Range[n], {k}]];
A002024[n_]:=Floor[1/2+Sqrt[2*n]];
A002260[n_]:=n-Binomial[Floor[1/2+Sqrt[2*n]], 2];
(* Linear *)
A096179[n_]:=A096179[n]=A096179[A002024[n], A002260[n]];
(* Enrique Pérez Herrero_, Dec 08 2010 *)

Prog

(PARI) A096179(n, k)={ my(m=lcm(vector(k, i, i))); forvec(v=vector(k-1, i, [2, n]), m>lcm(v) & m=lcm(v), 2); m } \\ M. F. Hasler, Nov 30 2010

Crossrefs

Main diagonal is A003418. Minimum in column k is A061799(k). See also A094348, A096180.

Sequence in context: A292901 A083773 A129116 * A361834 A166350 A357124

Adjacent sequences: A096176 A096177 A096178 * A096180 A096181 A096182

Keyword

nonn,tabl

Author

Matthew Vandermast, Jun 19 2004

Status

approved