A105606 Sylvester dividends for Pell numbers.

1, 1, 1, 2, 1, 10, 1, 12, 5, 58, 1, 420, 1, 338, 145, 408, 1, 13790, 1, 14268, 845, 11482, 1, 471240, 29, 66922, 985, 484692, 1, 111944350, 1, 470832, 28705, 2273378, 4901, 543353580, 1, 13250218, 167305, 543810552, 1, 129202326890, 1, 559334148, 38419925, 450117362

Offset: 1

Author

Paul Barry, Apr 15 2005

Keywords

• easy
• nonn

Comments

Divide each Pell number by its primitive part.

Crossrefs

Cf. A000129, A008555.

Programs

Mathematica

f[n_] := f[n] = Fibonacci[n, 2] / Product[f[d], {d, Most[Divisors[n]]}]; f[1] = 1; a[n_] := Fibonacci[n, 2]/f[n]; Array[a, 60] (* Amiram Eldar, Jun 20 2024 *)

Formula

a(n) = Pell(n)/A008555(n).

Extensions

More terms from Amiram Eldar, Jun 20 2024