|
%I #28 Jul 11 2022 16:04:48
%S 2,8,6,24,10,24,14,64,18,40,22,72,26,56,30,160,34,72,38,120,42,88,46,
%T 192,50,104,54,168,58,120,62,384,66,136,70,216,74,152,78,320,82,168,
%U 86,264,90,184,94,480,98,200,102,312,106,216,110,448,114,232,118,360,122
%N 2^a(n) divides (2n)^(2n): exponent of 2 in (2n)^(2n).
%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(n) = 2*n*A001511(n).
%F a(n) = A007814(A085534(n)). [corrected by _Kevin Ryde_, Oct 15 2021]
%F G.f.: Sum_{k>=0} 2^(k+1)*x^2^k/(1-x^2^k)^2. - _Ralf Stephan_, Jun 07 2003
%F a(n) = 2 * A091512(n). - _Alois P. Heinz_, Oct 14 2021
%p a:= 2*n*padic[ordp](2*n, 2):
%p seq(a(n), n=1..61); # _Alois P. Heinz_, Oct 14 2021
%t Table[ Part[ Flatten[ FactorInteger[n^n]], 2], {n, 2, 124, 2}]
%o (PARI) a(n) = n<<=1; n*valuation(n,2); \\ _Kevin Ryde_, Oct 14 2021
%o (Julia)
%o function A069895List(length)
%o a = zeros(Int, length)
%o for n in 1:length a[n] = 2 * (isodd(n) ? n : n + a[div(n, 2)]) end
%o a end
%o A069895List(61) |> println # _Peter Luschny_, Oct 16 2021
%o (Python)
%o def A069895(n): return n*(n&-n).bit_length()<<1 # _Chai Wah Wu_, Jul 11 2022
%Y Cf. A001511, A007814, A085534, A091512, A249153 (partial sums).
%K easy,nonn
%O 1,1
%A _Labos Elemer_, Apr 10 2002
|
