A120109 Row sums of number triangle A120108.

1, 3, 10, 21, 106, 107, 750, 1501, 4504, 4505, 49556, 49557, 644242, 644243, 644244, 1288489, 21904314, 21904315, 416181986, 416181987, 416181988, 416181989, 9572185748, 9572185749, 47860928746, 47860928747, 143582786242

Offset: 0

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• nonn

Comments

It appears that the indices k such that a(k) = a(k-1) + 1 are A080765. - Michel Marcus, Mar 04 2019

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A080765, A120108, A120110.

Programs

GAP

List([0..30],n->Sum([0..n],k->Lcm(List([1..n+1],i->i))/Lcm(List([1..k+1],i->i)))); # Muniru A Asiru, Mar 03 2019

Magma

A120108:= func< n,k | Lcm([1..n+1])/Lcm([1..k+1]) >;
[(&+[A120108(n,k): k in [0..n]]): n in [0..50]]; // G. C. Greubel, May 04 2023

Mathematica

A120108[n_, k_]:= LCM@@Range[n+1]/(LCM@@Range[k+1]);
A120109[n_]:= Sum[A120108[n, k], {k,0,n}];
Table[A120109[n], {n,0,50}] (* G. C. Greubel, May 04 2023 *)

PARI

a(n) = lcm([1..n+1])*sum(k=0, n, 1/lcm([1..k+1])); \\ Michel Marcus, Mar 04 2019

SageMath

def f(n): return lcm(range(1,n+2))
def A120109(n):
    return sum(f(n)//f(k) for k in range(n+1))
[A120109(n) for n in range(51)] # G. C. Greubel, May 04 2023

Formula

a(n) = Sum_{k=0..n} lcm(1,...,n+1)/lcm(1,...,k+1).