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

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• nonn
• tabl

Examples

			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;
		

Links

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

Crossrefs

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

Programs

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

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 *)

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

Formula

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