A120112 Row sums of number triangle A120111.

1, -1, -2, -1, -4, 0, -6, -1, -2, 0, -10, 0, -12, 0, 0, -1, -16, 0, -18, 0, 0, 0, -22, 0, -4, 0, -2, 0, -28, 0, -30, -1, 0, 0, 0, 0, -36, 0, 0, 0, -40, 0, -42, 0, 0, 0, -46, 0, -6, 0, 0, 0, -52, 0, 0, 0, 0, 0, -58, 0, -60, 0, 0, -1, 0, 0, -66, 0, 0, 0, -70, 0, -72

Offset: 0

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• sign

Comments

The last row of the columns in tables A133232 and A133233 are given by this sequence via the formula: if n < k + k*abs(a(n)) then k, otherwise 1 (1 <= k <= n). - Mats Granvik, Jan 22 2008

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A014963, A120111, A133232, A133233.

Programs

GAP

Concatenation([1],List([1..70],n->1-Lcm(List([1..n+1],i->i))/Lcm(List([1..n],i->i)))); # Muniru A Asiru, Mar 04 2019

Magma

A120112:= func< n | n eq 0 select 1 else 1-Lcm([1..n+1])/Lcm([1..n]) >;
[A120112(n): n in [0..100]]; // G. C. Greubel, May 05 2023

Mathematica

Table[If[n==0, 1, 1-LCM@@Range[n+1]/(LCM@@Range[n])], {n,0,100}] (* G. C. Greubel, May 05 2023 *)

PARI

a(n) = if (n==0, 1, 1 - lcm(vector(n+1, k, k))/lcm(vector(n, k, k))); \\ Michel Marcus, Sep 11 2016

SageMath

def A120112(n):
    return 1 if n == 0 else 1 - lcm(range(1,n+2)) // lcm(range(1,n+1))
[A120112(n) for n in range(101)] # G. C. Greubel, May 05 2023

Formula

a(n) = 1 - lcm(1,...,n+1)/lcm(1,...,n) for n > 0.

a(n) = 1 - A014963(n+1). - Joerg Arndt, Sep 12 2016