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A216957 a(1)=2; for n > 1, a(n) = 2^(n-2) + (1/(2n-2)) * Sum_{ d divides n-1 } phi(2d)*2^((n-1)/d).

%I A216957 #9 Sep 26 2012 12:13:19
%S A216957 2,2,4,6,12,20,40,74,148,286,568,1118,2228,4412,8788,17480,34836,
%T A216957 69392,138388,275942,550560,1098516,2192572,4376666,8738324,17448308,
%U A216957 34845304,69594398,139011816,277691852,554767744,1108378658,2214594580,4425117884,8842583584,17670722600,35314182976,70576759892,141055781836
%N A216957 a(1)=2; for n > 1, a(n) = 2^(n-2) + (1/(2n-2)) * Sum_{ d divides n-1 } phi(2d)*2^((n-1)/d).
%H A216957 N. J. A. Sloane, <a href="/A216957/b216957.txt">Table of n, a(n) for n = 1..1000</a>
%p A216957 with(numtheory);
%p A216957 f:=n-> if n=1 then 2 else 2^(n-2) + (1/(2*n-2)) * add(phi(2*d)*2^((n-1)/d), d in divisors(n-1)); fi;
%Y A216957 Different from, but easily confused with, A003000 and A122536.
%K A216957 nonn
%O A216957 1,1
%A A216957 _N. J. A. Sloane_, Sep 26 2012