A120106 a(n) = Sum_{k=0..n} lcm(1..2n+2)/lcm(1..2k+2).

1, 7, 36, 505, 1516, 16677, 216802, 433605, 7371286, 140054435, 140054436, 3221252029, 16106260146, 48318780439, 1401244632732, 86877167229385, 86877167229386, 86877167229387, 3214455187487320, 3214455187487321

Offset: 0

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• nonn

Examples

			a(2) = lcm(1,2,3,4,5,6)*(1/lcm(1,2) + 1/lcm(1,2,3,4) + 1/lcm(1,2,3,4,5,6)) = 60 (1/2 + 1/12 + 1/60) = 60 * 3/5 = 36. - _Bernard Schott_, Feb 27 2019
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..500

Crossrefs

Row sums of number triangle A120101.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> Lcm(List([1..2*n+2],i->i) )/Lcm(List([1..2*k+2],i->i)))); # Muniru A Asiru, Feb 26 2019

Magma

[(&+[ LCM([j: j in [1..2*n+2]])/LCM([j: j in [1..2*k+2]]): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Feb 26 2019

Mathematica

Table[Sum[(LCM@@Range[2n+2])/LCM@@Range[2k+2],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Mar 25 2012 *)

PARI

lcv(n) = lcm(vector(2*n+2, j, j));
a(n) = lcv(n)*sum(k=0, n, 1/lcv(k)); \\ Michel Marcus, Feb 27 2019

Sage

[sum(lcm(range(1,2*n+3))/lcm(range(1,2*k+3)) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Feb 26 2019