A067048 a(n) = lcm(n, n+1, n+2, n+3, n+4) / 60.
1, 1, 7, 14, 42, 42, 462, 66, 429, 1001, 1001, 364, 6188, 1428, 3876, 3876, 6783, 4389, 33649, 3542, 17710, 32890, 26910, 8190, 118755, 23751, 56637, 50344, 79112, 46376, 324632, 31416, 145299, 250971, 191919, 54834, 749398, 141778, 320866, 271502, 407253
Offset: 1
Examples
a(6) = 42 as lcm(6,7,8,9,10)/60 = 2520/60 = 42.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
- Amarnath Murthy, Some Notions on Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3 (Spring 2001), pp. 307-308.
- Index entries for linear recurrences with constant coefficients, 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).
- Index entries for sequences related to lcm's.
Programs
-
Maple
seq(ilcm(n,n+1,n+2,n+3,n+4)/60,n=1..100); # Robert Israel, Feb 07 2016
-
Mathematica
Table[LCM @@ Range[n, n + 4]/60, {n, 1, 50}] (* Amiram Eldar, Sep 29 2022 *) -
PARI
a(n)={lcm([n, n+1, n+2, n+3, n+4])/60} \\ Harry J. Smith, May 01 2010
Formula
From Gary Detlefs Apr 14 2011 and Apr 18 2011: (Start)
a(n) = (n+4)!*gcd(n-1,3)/(360*(n-1)!*gcd(n,4))
a(n) = (n+4)!*(5-4*cos((2*n+1)*Pi/3))/(1080*(n-1)!*(2+(-1)^n+cos(n*Pi/2)))
a(n) = (n+4)!*gcd(n-1,6)/(180*(n-1)!*2^((2*cos(n*Pi/2)+9+(-1)^n)/4)), n>1. (End)
120 <= n*(n+1)*(n+2)*(n+3)*(n+4)/a(n) <= 1440. - Charles R Greathouse IV, Sep 19 2012
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