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
KEYWORD
AUTHOR
Paul Barry, Jun 09 2006
STATUS
approved