A125605 -id:A125605 - cp's OEIS frontend

A125606 Row sums of A125605.

1, 2, 4, 8, 12, 18, 32, 40, 48, 58, 80, 92, 182, 292, 488, 686, 1056, 1702, 3384, 6306, 6312, 11208, 15396, 25438, 50724, 76456, 120836, 183926, 367712, 283100, 241562, 458512, 295752, 359288, 552162, 980830, 1605822, 2364730, 1862174, 3342496

Offset: 0

Franklin T. Adams-Watters, Nov 27 2006

nonn

Conjectures: a(n) acts like u^n, where u = 2 zeta(3) / zeta(2). In increasing order of strength: (1) lim_{n->infinity} a(n)^(1/n) = u; (2) lim_{n->infinity} a(n+1)/a(n) = u; (3) a(n) = c u^n + o(u^n) for some c. (Conjectures 2 and 3 are very speculative.)

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A125605, A000079.

A264856 Index of first row of triangle A125605 containing n.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 7, 6, 9, 10, 11, 8, 11, 10, 15, 16, 17, 18, 14, 12, 15, 22, 12, 18, 12, 22, 27, 18, 13, 20, 15, 32, 33, 34, 13, 36, 37, 14, 15, 14, 38, 42, 43, 44, 45, 16, 24, 13, 25, 50, 51, 52, 53, 54, 31, 56, 45, 58, 59, 60, 19, 62, 63, 64, 65, 66, 67

Offset: 1

Reinhard Zumkeller, Nov 26 2015

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A125605, A058084.

import Data.List (findIndex); import Data.Maybe (fromJust)
a264856 n = fromJust $ findIndex (elem n) a125605_tabl

A131134 a(1)=1. a(n) = (1/n + 1/a(n-1)) * lcm(n,a(n-1)).

Original entry on oeis.org

1, 3, 2, 3, 8, 7, 2, 5, 14, 12, 23, 35, 48, 31, 46, 31, 48, 11, 30, 5, 26, 24, 47, 71, 96, 61, 88, 29, 2, 16, 47, 79, 112, 73, 108, 4, 41, 79, 118, 79, 120, 27, 70, 57, 34, 40, 87, 45, 94, 72, 41, 93, 146, 100, 31, 87, 48, 53, 112, 43, 104, 83, 146, 105, 34, 50, 117, 185, 254

Offset: 1

Leroy Quet, Jun 17 2007

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A131133.

Equals T(n+1,2) for the Adams-Watters triangle, A125605. - Gerry Myerson, Mar 18 2010

a131134 n = a131134_list !! (n-1)
a131134_list = 1 : zipWith (\v w -> (v+w) `div` gcd v w) [2..] a131134_list
-- Reinhard Zumkeller, Nov 26 2015

A131134 := proc(n) option remember ; if n = 1 then 1; else (1/n+1/A131134(n-1))*lcm(n,A131134(n-1)) ; fi ; end: seq(A131134(n),n=1..80) ; # R. J. Mathar, Oct 17 2007

nxt[{n_,a_}]:={n+1,(1/(n+1)+1/a)LCM[n+1,a]}; Transpose[NestList[nxt,{1,1},70]][[2]] (* Harvey P. Dale, Aug 13 2013 *)

For n > 1: a(n) = (n + a(n-1)) / GCD(n, a(n-1)). - Reinhard Zumkeller, Nov 26 2015

More terms from R. J. Mathar, Oct 17 2007

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A125606 Row sums of A125605.

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A264856 Index of first row of triangle A125605 containing n.

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A131134 a(1)=1. a(n) = (1/n + 1/a(n-1)) * lcm(n,a(n-1)).

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