OFFSET
0,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/2)} lcm(1,..,n-k+1)/lcm(1,..,k+1).
MATHEMATICA
A120108[n_, k_]:= LCM@@Range[n+1]/(LCM@@Range[k+1]);
Table[A120110[n], {n, 0, 50}] (* G. C. Greubel, May 04 2023 *)
PROG
(GAP) List([0..30], n->Sum([0..Int(n/2)], k->Lcm(List([1..n-k+1], i->i))/Lcm(List([1..k+1], i->i)))); # Muniru A Asiru, Mar 04 2019
(PARI) a(n) = sum(k=0, n\2, lcm([1..n-k+1])/lcm([1..k+1])); \\ Michel Marcus, Mar 04 2019
(Magma)
A120108:= func< n, k | Lcm([1..n+1])/Lcm([1..k+1]) >;
[(&+[A120108(n-k, k): k in [0..Floor(n/2)]]): n in [0..50]]; # G. C. Greubel, May 04 2023
(SageMath)
def f(n): return lcm(range(1, n+2))
def A120110(n):
return sum(f(n-k)//f(k) for k in range((n//2)+1))
[A120110(n) for n in range(51)] # G. C. Greubel, May 04 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 09 2006
STATUS
approved