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A096179
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Triangle read by rows: T(n,k) is the smallest positive integer having at least k of the first n positive integers as divisors.
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7
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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; internal format)
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OFFSET
| 1,3
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LINKS
| Wikipedia, Table of divisors.
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FORMULA
| T(n,k) = min { lcm(x_1,...,x_k) ; 0 < x_1 < ... < x_k <= n }
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EXAMPLE
| Triangle begins:
1
1 2
1 2 6
1 2 4 12
1 2 4 12 60
1 2 4 6 12 60
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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 6 2010
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MATHEMATICA
| Contribution from Enrique Perez Herrero (psychgeometry(AT)gmail.com), Dec 08 2010:
(* 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]];
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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
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CROSSREFS
| Main diagonal is A003418. Minimum in column k is A061799(k). See also A094348, A096180.
Sequence in context: A178803 A083773 A129116 * A166350 A133643 A008305
Adjacent sequences: A096176 A096177 A096178 * A096180 A096181 A096182
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KEYWORD
| nonn,tabl
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AUTHOR
| Matthew Vandermast (ghodges14(AT)comcast.net), Jun 19, 2004
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