cp's OEIS Frontend

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.

%I A096179 #24 Mar 13 2014 10:11:19
%S A096179 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,
%T A096179 4,6,12,24,120,840,1,2,4,6,12,24,72,360,2520,1,2,4,6,12,24,60,120,360,
%U A096179 2520,1,2,4,6,12,24,60,120,360,2520,27720,1,2,4,6,12,12,24,60,120,360
%N 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.
%H A096179 Wikipedia, <a href="http://en.wikipedia.org/wiki/Table_of_divisors">Table of divisors</a>.
%F A096179 T(n,k) = min { lcm(x_1,...,x_k) ; 0 < x_1 < ... < x_k <= n }
%e A096179 Triangle begins:
%e A096179 1
%e A096179 1 2
%e A096179 1 2 6
%e A096179 1 2 4 12
%e A096179 1 2 4 12 60
%e A096179 1 2 4  6 12 60
%p A096179 with(combstruct):
%p A096179 a096179_row := proc(n) local k,L,l,R,LCM,comb;
%p A096179 R := NULL; LCM := ilcm(seq(i,i=[$1..n]));
%p A096179 for k from 1 to n-1 do
%p A096179    L := LCM;
%p A096179    comb := iterstructs(Combination(n),size=k):
%p A096179    while not finished(comb) do
%p A096179       l := nextstruct(comb);
%p A096179       L := min(L,ilcm(op(l)));
%p A096179    od;
%p A096179    R := R,L;
%p A096179 od;
%p A096179 R,LCM end; # _Peter Luschny_, Dec 06 2010
%t A096179 (* Triangular *)
%t A096179 A096179[n_,k_]:=Min[LCM@@@Subsets[Range[n],{k}]];
%t A096179 A002024[n_]:=Floor[1/2+Sqrt[2*n]];
%t A096179 A002260[n_]:=n-Binomial[Floor[1/2+Sqrt[2*n]],2];
%t A096179 (* Linear *)
%t A096179 A096179[n_]:=A096179[n]=A096179[A002024[n],A002260[n]];
%t A096179 (* Enrique Pérez Herrero_, Dec 08 2010 *)
%o A096179 (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
%Y A096179 Main diagonal is A003418. Minimum in column k is A061799(k). See also A094348, A096180.
%K A096179 nonn,tabl
%O A096179 1,3
%A A096179 _Matthew Vandermast_, Jun 19 2004