%I A091512
%S A091512 1,4,3,12,5,12,7,32,9,20,11,36,13,28,15,80,17,36,19,60,21,44,23,96,25,
%T A091512 52,27,84,29,60,31,192,33,68,35,108,37,76,39,160,41,84,43,132,45,92,47,
%U A091512 240,49,100,51,156,53,108,55,224,57,116,59,180,61,124,63
%N A091512 2^a(n) divides (2n)^n: exponent of 2 in (2n)^n.
%F A091512 a(n) = A007814(A000312(n)) = n*A001511(n) = A069895(n)/2.
%F A091512 G.f.: sum(k>=0, 2^k*x^2^k/(1-x^2^k)^2).
%F A091512 Recurrence: a(0) = 0, a(2n) = 2a(n) + 2n, a(2n+1) = 2n+1.
%F A091512 Dirichlet g.f.: zeta(s-1)*2^s/(2^s-2). - Ralf Stephan, Jun 17 2007
%F A091512 Mobius transform of A162728, where x/(1-x)^2 = Sum_{n>=1} A162728(n)*x^n/
               (1+x^n). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
%F A091512 a(n) = A162728(2n)/phi(2n), where x/(1-x)^2 = Sum_{n>=1} A162728(n)*x^n/
               (1+x^n). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
%t A091512 Table[ Part[ Flatten[ FactorInteger[2n^n]], 2], {n, 1, 124}]
%o A091512 (PARI) a(n)=n*(valuation(n,2)+1)
%o A091512 (PARI) a(n)=if(n<1,0,if(n%2==0,2*a(n/2)+n,n))
%Y A091512 Cf. A091519, A090740, A090739.
%Y A091512 Cf. A162728. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 12 2009]
%Y A091512 Sequence in context: A126604 A099377 A121844 this_sequence A106285 A061727 
               A055527
%Y A091512 Adjacent sequences: A091509 A091510 A091511 this_sequence A091513 A091514 
               A091515
%K A091512 nonn,easy
%O A091512 1,2
%A A091512 R. Stephan (ralf(AT)ark.in-berlin.de) and Labos E. (labos(AT)ana.sote.hu), 
               Jan 18 2004