A120108 Number triangle T(n,k) = lcm(1,..,n+1)/lcm(1,..,k+1).

1, 2, 1, 6, 3, 1, 12, 6, 2, 1, 60, 30, 10, 5, 1, 60, 30, 10, 5, 1, 1, 420, 210, 70, 35, 7, 7, 1, 840, 420, 140, 70, 14, 14, 2, 1, 2520, 1260, 420, 210, 42, 42, 6, 3, 1, 2520, 1260, 420, 210, 42, 42, 6, 3, 1, 1, 27720, 13860, 4620, 2310, 462, 462, 66, 33, 11, 11, 1

Offset

0,2

Links

Muniru A Asiru, Rows n=0..100 of triangle, flattened

Formula

Number triangle T(n,k) = [k<=n]*lcm(1,..,n+1)/lcm(1,..,k+1).

Example

Triangle begins:
    1;
    2,   1;
    6,   3,  1;
   12,   6,  2,  1;
   60,  30, 10,  5, 1;
   60,  30, 10,  5, 1, 1;
  420, 210, 70, 35, 7, 7, 1;

Maple

T:= (n, k)-> ilcm(seq(q, q=1..n+1))/ilcm(seq(r, r=1..k+1)):
seq(seq(T(n, k), k=0..n), n=0..10); # Muniru A Asiru, Feb 26 2019

Mathematica

f[n_] := f[n] = LCM @@ Range[n];
T[n_, k_] := f[n+1]/f[k+1];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Mar 01 2021 *)

Prog

(GAP) Flat(List([0..10], n->List([0..n], k->Lcm(List([1..n+1], i->i))/Lcm(List([1..k+1], i->i))))); # Muniru A Asiru, Feb 26 2019
(Magma)
A120108:= func< n, k | Lcm([1..n+1])/Lcm([1..k+1]) >;
[A120108(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 04 2023
(SageMath)
def f(n): return lcm(range(1, n+2))
def A120108(n, k):
    return f(n)/f(k)
flatten([[A120108(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, May 04 2023

Crossrefs

First column is A003418(n+1). Second column is A025555. Row sums are A120109. Diagonal sums are A120110. Inverse is A120111.

Sequence in context: A142977 A356601 A362997 * A350292 A060556 A222969

Adjacent sequences: A120105 A120106 A120107 * A120109 A120110 A120111

Keyword

easy,nonn,tabl

Author

Paul Barry, Jun 09 2006

Status

approved