%I #9 Feb 06 2020 14:50:14

%S 1,0,1,3,7,14,31,60,126,248,511,1005,2047,4064,8183,16320,32767,65394,

%T 131071,261885,524255,1048064,2097151,4193220,8388600,16775168,

%U 33554304,67104765,134217727,268427002,536870911,1073725440,2147483135

%N a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1).

%C Triangle A123706 is the matrix inverse of triangle A010766(n,k) = [n/k].

%H G. C. Greubel, <a href="/A123707/b123707.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{k>=1} mu(k) * x^k * (1 - x^k) / (1 - 2*x^k). - _Ilya Gutkovskiy_, Feb 06 2020

%t t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Oct 26 2017 *)

%o (PARI) {a(n)=sum(k=1,n,(matrix(n,n,r,c,if(r>=c,floor(r/c)))^-1)[n,k]*2^(k-1))}

%Y Cf. A123706, A123708, A123709.

%K nonn

%O 1,4

%A _Paul D. Hanna_, Oct 09 2006