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

0,2

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

Formula

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

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 *)

Prog

(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
(PARI) a(n) = lcm([1..n+1])*sum(k=0, n, 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 in [0..n]]): n in [0..50]]; // G. C. Greubel, May 04 2023
(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

Crossrefs

Cf. A080765, A120108, A120110.

Sequence in context: A071563 A360632 A139116 * A286067 A337623 A158030

Adjacent sequences: A120106 A120107 A120108 * A120110 A120111 A120112

Keyword

easy,nonn

Author

Paul Barry, Jun 09 2006

Status

approved