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

Author

Matthew Vandermast, Jun 19 2004

Keywords

• nonn
• tabl

Examples

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

Links

• Wikipedia, Table of divisors.

Crossrefs

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

Programs

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 *)

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

Formula

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