A131134 -id:A131134 - cp's OEIS frontend

A125605 Triangle read by rows: T(n,k) = (T(n-1,k-1) + T(n-1,k)) / gcd(T(n-1,k-1), T(n-1,k)).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 2, 4, 1, 1, 5, 3, 3, 5, 1, 1, 6, 8, 2, 8, 6, 1, 1, 7, 7, 5, 5, 7, 7, 1, 1, 8, 2, 12, 2, 12, 2, 8, 1, 1, 9, 5, 7, 7, 7, 7, 5, 9, 1, 1, 10, 14, 12, 2, 2, 2, 12, 14, 10, 1, 1, 11, 12, 13, 7, 2, 2, 7, 13, 12, 11, 1, 1, 12, 23, 25, 20, 9, 2, 9, 20, 25, 23, 12, 1, 1, 13

Offset: 0

Franklin T. Adams-Watters, Nov 27 2006

Row A264856(n) contains the first occurrence of n, n > 0. - Reinhard Zumkeller, Nov 26 2015

T. D. Noe, Rows n=0..100, flattened

Cf. A007318, A125606.

Cf. A040000 (central terms), A131134, A264856.

a125605 n k = a125605_tabl !! n !! k
a125605_row n = a125605_tabl !! n
a125605_tabl = iterate f [1] where
   f xs = zipWith (\v w -> (v + w) `div` gcd v w) ([0] ++ xs) (xs ++ [0])
-- Reinhard Zumkeller, Nov 26 2015

A131133 a(0)=1; for n > 0, a(n) = (1/n + 1/a(n-1))*lcm(n, a(n-1)).

Original entry on oeis.org

1, 2, 2, 5, 9, 14, 10, 17, 25, 34, 22, 3, 5, 18, 16, 31, 47, 64, 41, 60, 4, 25, 47, 70, 47, 72, 49, 76, 26, 55, 17, 48, 5, 38, 36, 71, 107, 144, 91, 10, 5, 46, 44, 87, 131, 176, 111, 158, 103, 152, 101, 152, 51, 104, 79, 134, 95, 8, 33, 92, 38, 99, 161, 32, 3, 68, 67, 2, 35, 104

Offset: 0

Leroy Quet, Jun 17 2007

nonn

Equivalently, a(0)=1; a(n) = (a(n-1)+n)/gcd(n,a(n-1)). - Ctibor O. Zizka, Feb 15 2008

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A131134.

a[0] := 1; for n to 70 do a[n] := (1/n+1/a[n-1])*lcm(n, a[n-1]) end do; seq(a[n], n = 0 .. 70) # Emeric Deutsch, Jun 21 2007

nxt[{n_,a_}]:={n+1,(1/(n+1)+1/a)LCM[n+1,a]}; Transpose[NestList[nxt,{0,1},70]][[2]] (* Harvey P. Dale, Mar 04 2013 *)

More terms from Emeric Deutsch, Jun 21 2007

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar

cp's OEIS Frontend

A125605 Triangle read by rows: T(n,k) = (T(n-1,k-1) + T(n-1,k)) / gcd(T(n-1,k-1), T(n-1,k)).

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