|
%I #29 Sep 08 2022 08:45:25
%S 1,7,36,505,1516,16677,216802,433605,7371286,140054435,140054436,
%T 3221252029,16106260146,48318780439,1401244632732,86877167229385,
%U 86877167229386,86877167229387,3214455187487320,3214455187487321
%N a(n) = Sum_{k=0..n} lcm(1..2n+2)/lcm(1..2k+2).
%H Muniru A Asiru, <a href="/A120106/b120106.txt">Table of n, a(n) for n = 0..500</a>
%e 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
%t Table[Sum[(LCM@@Range[2n+2])/LCM@@Range[2k+2],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Mar 25 2012 *)
%o (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
%o (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
%o (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
%o (PARI) lcv(n) = lcm(vector(2*n+2, j, j));
%o a(n) = lcv(n)*sum(k=0, n, 1/lcv(k)); \\ _Michel Marcus_, Feb 27 2019
%Y Row sums of number triangle A120101.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 09 2006
|
