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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 PĂ©rez 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 * A166350 A210227 A208757

Adjacent sequences:  A096176 A096177 A096178 * A096180 A096181 A096182

KEYWORD

nonn,tabl

AUTHOR

Matthew Vandermast, Jun 19 2004

STATUS

approved

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Last modified May 25 01:56 EDT 2019. Contains 323534 sequences. (Running on oeis4.)