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

%I A069895 #33 Sep 13 2024 06:57:58
%S A069895 2,8,6,24,10,24,14,64,18,40,22,72,26,56,30,160,34,72,38,120,42,88,46,
%T A069895 192,50,104,54,168,58,120,62,384,66,136,70,216,74,152,78,320,82,168,
%U A069895 86,264,90,184,94,480,98,200,102,312,106,216,110,448,114,232,118,360,122
%N A069895 2^a(n) divides (2n)^(2n): exponent of 2 in (2n)^(2n).
%H A069895 Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences with (relatively) simple ordinary generating functions</a>, 2004.
%H A069895 Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>.
%F A069895 a(n) = 2*n*A001511(n).
%F A069895 a(n) = A007814(A085534(n)). [corrected by _Kevin Ryde_, Oct 15 2021]
%F A069895 G.f.: Sum_{k>=0} 2^(k+1)*x^2^k/(1-x^2^k)^2. - _Ralf Stephan_, Jun 07 2003
%F A069895 a(n) = 2 * A091512(n). - _Alois P. Heinz_, Oct 14 2021
%F A069895 Sum_{k=1..n} a(k) ~ 2*n^2. - _Amiram Eldar_, Sep 13 2024
%p A069895 a:= 2*n*padic[ordp](2*n, 2):
%p A069895 seq(a(n), n=1..61);  # _Alois P. Heinz_, Oct 14 2021
%t A069895 Table[ Part[ Flatten[ FactorInteger[n^n]], 2], {n, 2, 124, 2}]
%o A069895 (PARI) a(n) = n<<=1; n*valuation(n,2); \\ _Kevin Ryde_, Oct 14 2021
%o A069895 (Julia)
%o A069895 function A069895List(length)
%o A069895     a = zeros(Int, length)
%o A069895     for n in 1:length a[n] = 2 * (isodd(n) ? n : n + a[div(n, 2)]) end
%o A069895 a end
%o A069895 A069895List(61) |> println # _Peter Luschny_, Oct 16 2021
%o A069895 (Python)
%o A069895 def A069895(n): return n*(n&-n).bit_length()<<1 # _Chai Wah Wu_, Jul 11 2022
%Y A069895 Cf. A001511, A007814, A085534, A091512, A249153 (partial sums).
%K A069895 easy,nonn
%O A069895 1,1
%A A069895 _Labos Elemer_, Apr 10 2002