A189046 a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5)/60.

0, 1, 7, 14, 42, 42, 462, 462, 858, 3003, 1001, 4004, 6188, 18564, 27132, 3876, 27132, 74613, 100947, 67298, 17710, 230230, 296010, 188370, 237510, 118755, 736281, 453096, 553784, 1344904, 324632

Offset

0,3

Comments

a(n) mod 2 has a period of 8, repeating [0,1,1,0,0,0,0,0].

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 7, 0, 0, 0, 0, -28, 0, 0, 0, 0, 84, 0, 0, 0, 0, -203, 0, 0, 0, 0, 413, 0, 0, 0, 0, -728, 0, 0, 0, 0, 1128, 0, 0, 0, 0, -1554, 0, 0, 0, 0, 1918, 0, 0, 0, 0, -2128, 0, 0, 0, 0, 2128, 0, 0, 0, 0, -1918, 0, 0, 0, 0, 1554, 0, 0, 0, 0, -1128, 0, 0, 0, 0, 728, 0, 0, 0, 0, -413, 0, 0, 0, 0, 203, 0, 0, 0, 0, -84, 0, 0, 0, 0, 28, 0, 0, 0, 0, -7, 0, 0, 0, 0, 1).

Index entries for sequences related to lcm's.

Formula

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(4*(n^4 mod 5)+1)/(1800*((n^3 mod 4)+((n-1)^3 mod 4)+1)).

a(n) = binomial(n+5,6)/(gcd(n,5)*(A021913(n-1)+1)).

a(n) = binomial(n+5,6)/(gcd(n,5)*floor(((n-1) mod 4)/2+1)). - Gary Detlefs, Apr 22 2011

Sum_{n>=1} 1/a(n) = 92 + (54/5-18*sqrt(5)+6*sqrt(178-398/sqrt(5)))*Pi. - Amiram Eldar, Sep 29 2022

Maple

seq(lcm(n, n+1, n+2, n+3, n+4, n+5)/60, n=0..30)

Mathematica

Table[(LCM@@(n+Range[0, 5]))/60, {n, 0, 40}]  (* Harvey P. Dale, Apr 17 2011 *)

Prog

(PARI) a(n)=lcm([n..n+5])/60 \\ Charles R Greathouse IV, Sep 30 2016

Crossrefs

Cf. A000217 ( = lcm(n,n+1)/2), A021913, A067046, A067047, A067048.

Sequence in context: A161814 A333594 A067048 * A098328 A062098 A045759

Adjacent sequences: A189043 A189044 A189045 * A189047 A189048 A189049

Keyword

nonn,easy

Author

Gary Detlefs, Apr 15 2011

Status

approved