%I #21 Jul 14 2023 09:02:06
%S 2,8,12,32,40,96,140,320,540,1120,2068,4320,8216,16688,32880,66176,
%T 131104,263376,524324,1050880,2097480,4198480,8388652,16786368,
%U 33554600,67125344,134218836,268468928,536870968,1073809920,2147483708,4295099648,8589938808,17180131456,34359739120,68720011776
%N a(n) = Sum_{d|n} 2^d*phi(2*n/d).
%H Michael De Vlieger, <a href="/A306898/b306898.txt">Table of n, a(n) for n = 1..3321</a>
%H Dennis S. Bernstein, Omran Kouba, <a href="https://arxiv.org/abs/1901.10703">Counting Colorful Necklaces and Bracelets in Three Colors</a>, arXiv:1901.10703 [math.CO], 2019.
%F a(n) = 2 * n * A000013(n). - _Seiichi Manyama_, Jul 14 2023
%p See A306888.
%t Table[DivisorSum[n, 2^# *EulerPhi[2 n/#] &], {n, 36}] (* _Michael De Vlieger_, Mar 18 2019 *)
%o (PARI) a(n) = sumdiv(n, d, 2^d*eulerphi(2*n/d)); \\ _Michel Marcus_, Mar 16 2019
%Y Cf. A000013, A306888, A306896, A306905.
%K nonn
%O 1,1
%A _Michael De Vlieger_ and _N. J. A. Sloane_, Mar 15 2019