A067048 - OEIS

%I #35 Sep 29 2022 03:29:57

%S 1,1,7,14,42,42,462,66,429,1001,1001,364,6188,1428,3876,3876,6783,

%T 4389,33649,3542,17710,32890,26910,8190,118755,23751,56637,50344,

%U 79112,46376,324632,31416,145299,250971,191919,54834,749398,141778,320866,271502,407253

%N a(n) = lcm(n, n+1, n+2, n+3, n+4) / 60.

%H Harry J. Smith, <a href="/A067048/b067048.txt">Table of n, a(n) for n = 1..1000</a>

%H Amarnath Murthy, <a href="http://fs.unm.edu/SN/SomeNotionsLeast.pdf">Some Notions on Least Common Multiples</a>, Smarandache Notions Journal, Vol. 12, No. 1-2-3 (Spring 2001), pp. 307-308.

%H <a href="/index/Rec#order_72">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.

%F From _Gary Detlefs_ Apr 14 2011 and Apr 18 2011: (Start)

%F a(n) = (n+4)!*gcd(n-1,3)/(360*(n-1)!*gcd(n,4))

%F a(n) = (n+4)!*(5-4*cos((2*n+1)*Pi/3))/(1080*(n-1)!*(2+(-1)^n+cos(n*Pi/2)))

%F a(n) = (n+4)!*gcd(n-1,6)/(180*(n-1)!*2^((2*cos(n*Pi/2)+9+(-1)^n)/4)), n>1. (End)

%F 120 <= n*(n+1)*(n+2)*(n+3)*(n+4)/a(n) <= 1440. - _Charles R Greathouse IV_, Sep 19 2012

%F Sum_{n>=1} 1/a(n) = 80 - 40*log(sqrt(3)+2)/sqrt(3) - 490*log(2)/3 + 60*log(3). - _Amiram Eldar_, Sep 29 2022

%e a(6) = 42 as lcm(6,7,8,9,10)/60 = 2520/60 = 42.

%p seq(ilcm(n,n+1,n+2,n+3,n+4)/60,n=1..100); # _Robert Israel_, Feb 07 2016

%t Table[LCM @@ Range[n, n + 4]/60, {n, 1, 50}] (* _Amiram Eldar_, Sep 29 2022 *)

%o (PARI) { for (n=1, 1000, write("b067048.txt", n, " ", lcm(lcm(lcm(n,n+1), lcm(n+2,n+3)), n+4)/60) ) } \\ _Harry J. Smith_, May 01 2010

%Y Cf. A067046, A067047.

%K nonn,easy,less

%O 1,3

%A _Amarnath Murthy_, Dec 30 2001