A208449 Numerator of A010786(n+1) / A010786(n).

2, 3, 8, 5, 18, 7, 64, 27, 25, 11, 288, 13, 98, 225, 1024, 17, 729, 19, 2000, 147, 242, 23, 55296, 125, 169, 729, 10976, 29, 1125, 31, 32768, 1089, 289, 1225, 209952, 37, 722, 507, 640000, 41, 64827, 43, 42592, 91125, 1058, 47, 14155776, 343, 15625, 2601

Offset: 1

Author

Reinhard Zumkeller, Feb 26 2012

Keywords

• nonn
• frac

Links

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

Crossrefs

Cf. A208450 (denominator).

Cf. A010786, A208448.

Cf. A007955, A377484.

Programs

Haskell

import Data.Ratio ((%), numerator)
a208449 n = a208449_list !! (n-1)
a208449_list = map numerator $
   zipWith (%) (tail a010786_list) a010786_list

Mathematica

A208449[n_] := Times @@ # / GCD[Times @@ #, Times @@ (# - 1)] & [Rest[Divisors[n + 1]]];
Array[A208449, 100] (* Paolo Xausa, Feb 20 2025 *)

PARI

f(n) = prod(k=1, n, n\k); \\ A010786
a(n) = numerator(f(n+1)/f(n)); \\ Michel Marcus, Feb 08 2025

Formula

a(n) = A010786(n+1) / A208448(n).

a(n) = A007955(n+1)/gcd(A007955(n+1), A377484(n+1)). - Ridouane Oudra, Feb 03 2025