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%I #12 Mar 27 2017 09:10:39
%S 1,0,0,2,0,2,4,2,0,8,4,2,16,2,4,38,0,2,64,2,16,134,4,2,256,32,4,512,
%T 16,2,1084,2,0,2054,4,158,4096,2,4,8198,256,2,16444,2,16,33272,4,2,
%U 65536,128,1024,131078,16,2,262144,2078,256,524294,4,2,1052656,2,4,2097656,0,8222,4194364,2,16,8388614,17404,2,16777216,2,4,33587168,16,2174,67108924
%N a(n) = 2^n - 2*n*A000048(n).
%C a(n) = total length of all cycles (see A000048) which are strictly less than the full length of 2n.
%D R. K. Guy, Posting to Sequence Fans Mailing List, Apr 20 2012
%H Alois P. Heinz, <a href="/A182256/b182256.txt">Table of n, a(n) for n = 0..2000</a>
%p with (numtheory):
%p a:= n-> 2^n -add (mobius(d)*2^(n/d), d=select(x->is(x, odd), divisors(n))):
%p seq (a(n), n=0..80); # _Alois P. Heinz_, Apr 21 2012
%t a[n_] := 2^n - DivisorSum[n, Mod[#, 2]*MoebiusMu[#]*2^(n/#)&]; a[0] = 1;
%t Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Mar 27 2017 *)
%Y Cf. A000048.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Apr 21 2012
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