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

1,3

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.

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A067046, A067047.

Sequence in context: A055780 A161814 A333594 * A189046 A098328 A062098

Adjacent sequences: A067045 A067046 A067047 * A067049 A067050 A067051

Keyword

nonn,easy,less

Author

Amarnath Murthy, Dec 30 2001

Status

approved