A245392 Sum_{k, k|n} 2^(k-1) + Sum_{1<=k<=n, gcd(k,n)=1} 2^(k-1).

2, 4, 8, 16, 32, 56, 128, 224, 480, 856, 2048, 3200, 8192, 13656, 29920, 54752, 131072, 202104, 524288, 857952, 1939168, 3495256, 8388608, 12918016, 33013248, 55924056, 124631008, 222655840, 536870912, 809850488, 2147483648, 3579172320, 7974270688, 14316557656

Offset: 1

Author

Michel Marcus, Jul 21 2014

Keywords

• nonn

Comments

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

Crossrefs

Cf. A034729, A054432.

Programs

Maple

f:= proc(k,n) local g; g:= igcd(k,n); g = 1 or g = k end proc:
A:= n -> 1 + add(2^(k-1),k=select(f,[$1..n],n));
seq(A(n),n=1..100); # Robert Israel, Jul 21 2014

PARI

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

Formula

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

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