A069895 2^a(n) divides (2n)^(2n): exponent of 2 in (2n)^(2n).

2, 8, 6, 24, 10, 24, 14, 64, 18, 40, 22, 72, 26, 56, 30, 160, 34, 72, 38, 120, 42, 88, 46, 192, 50, 104, 54, 168, 58, 120, 62, 384, 66, 136, 70, 216, 74, 152, 78, 320, 82, 168, 86, 264, 90, 184, 94, 480, 98, 200, 102, 312, 106, 216, 110, 448, 114, 232, 118, 360, 122

Offset: 1

Author

Labos Elemer, Apr 10 2002

Keywords

• easy
• nonn

Links

• Ralf Stephan, Some divide-and-conquer sequences with (relatively) simple ordinary generating functions, 2004.
• Ralf Stephan, Table of generating functions.

Crossrefs

Cf. A001511, A007814, A085534, A091512, A249153 (partial sums).

Programs

Julia

function A069895List(length)
    a = zeros(Int, length)
    for n in 1:length a[n] = 2 * (isodd(n) ? n : n + a[div(n, 2)]) end
a end
A069895List(61) |> println # Peter Luschny, Oct 16 2021

Maple

a:= 2*n*padic[ordp](2*n, 2):
seq(a(n), n=1..61);  # Alois P. Heinz, Oct 14 2021

Mathematica

Table[ Part[ Flatten[ FactorInteger[n^n]], 2], {n, 2, 124, 2}]

PARI

a(n) = n<<=1; n*valuation(n,2); \\ Kevin Ryde, Oct 14 2021

Python

def A069895(n): return n*(n&-n).bit_length()<<1 # Chai Wah Wu, Jul 11 2022

Formula

a(n) = 2*n*A001511(n).

a(n) = A007814(A085534(n)). [corrected by Kevin Ryde, Oct 15 2021]

G.f.: Sum_{k>=0} 2^(k+1)*x^2^k/(1-x^2^k)^2. - Ralf Stephan, Jun 07 2003

a(n) = 2 * A091512(n). - Alois P. Heinz, Oct 14 2021

Sum_{k=1..n} a(k) ~ 2*n^2. - Amiram Eldar, Sep 13 2024