A245392 - OEIS

%I #13 Aug 01 2019 03:49:34

%S 2,4,8,16,32,56,128,224,480,856,2048,3200,8192,13656,29920,54752,

%T 131072,202104,524288,857952,1939168,3495256,8388608,12918016,

%U 33013248,55924056,124631008,222655840,536870912,809850488,2147483648,3579172320,7974270688,14316557656

%N Sum_{k, k|n} 2^(k-1) + Sum_{1<=k<=n, gcd(k,n)=1} 2^(k-1).

%C The 1's in the binary expansion of 2^n - a(n) correspond to k such that 1 < gcd(k,n) < k < n. - _Robert Israel_, Jul 21 2014

%F a(n) = A034729(n) + A054432(n).

%F If p is prime a(p) = 2^p.

%p f:= proc(k,n) local g; g:= igcd(k,n); g = 1 or g = k end proc:

%p A:= n -> 1 + add(2^(k-1),k=select(f,[$1..n],n));

%p seq(A(n),n=1..100); # _Robert Israel_, Jul 21 2014

%o (PARI) sum(k=1, n, if (gcd(k,n)==1, 2^(k-1), 0)) + sumdiv(n, k, k*2^(k-1));

%Y Cf. A034729, A054432.

%K nonn

%O 1,1

%A _Michel Marcus_, Jul 21 2014