A067048 -id:A067048 - cp's OEIS frontend

A067049 Triangle T(n,r) = lcm(n,n-1,n-2,...,n-r+1)/lcm(1,2,3,...,r-1,r), 0 <= r < n.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 10, 5, 1, 1, 1, 7, 21, 35, 35, 7, 7, 1, 1, 8, 28, 28, 70, 14, 14, 2, 1, 1, 9, 36, 84, 42, 42, 42, 6, 3, 1, 1, 10, 45, 60, 210, 42, 42, 6, 3, 1, 1, 1, 11, 55, 165, 330, 462, 462, 66, 33, 11, 11, 1, 1, 12, 66, 110

Offset: 0

Amarnath Murthy, Dec 30 2001

			Triangle begins:
  1;
  1, 1;
  1, 2, 1;
  1, 3, 3, 1;
  1, 4, 6, 2, 1; ...

Amarnath Murthy, Some Notions on Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.

Diagonals give A067046, A067047, A067048. Row sums give A061297.

t[n_, r_] :=  LCM @@ Table[n-k+1, {k, 1, r}] / LCM @@ Table[k, {k, 1, r}]; t[, 0] = 1; Table[t[n, r], {n, 0, 12}, {r, 0, n}] // Flatten (* _Jean-François Alcover, Apr 22 2014 *)

t(n, r) = {nt = 1; for (k = n-r+1, n, nt = lcm(nt, k);); dt = 1; for (k = 1, r, dt = lcm(dt, k);); return (nt/dt);} \\ Michel Marcus, Sep 14 2013

More terms from Vladeta Jovovic, Dec 31 2001

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

Original entry on oeis.org

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

Gary Detlefs, Apr 15 2011

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

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.

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

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

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

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

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

cp's OEIS Frontend

A067049 Triangle T(n,r) = lcm(n,n-1,n-2,...,n-r+1)/lcm(1,2,3,...,r-1,r), 0 <= r < n.

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

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