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

1,1

Links

Table of n, a(n) for n=1..61.

Ralf Stephan, Some divide-and-conquer sequences ...

Ralf Stephan, Table of generating functions

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

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}]

Prog

(PARI) a(n) = n<<=1; n*valuation(n, 2); \\ Kevin Ryde, Oct 14 2021
(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
(Python)
def A069895(n): return n*(n&-n).bit_length()<<1 # Chai Wah Wu, Jul 11 2022

Crossrefs

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

Sequence in context: A100871 A111860 A278160 * A370925 A085590 A079538

Adjacent sequences: A069892 A069893 A069894 * A069896 A069897 A069898

Keyword

easy,nonn

Author

Labos Elemer, Apr 10 2002

Status

approved