A306899 a(n) = Sum_{d|n} (2^d - (-1)^d)*phi(3*n/d).

6, 12, 36, 48, 90, 180, 294, 576, 1134, 2160, 4158, 8496, 16458, 33096, 65880, 131712, 262242, 525852, 1048686, 2099520, 4195296, 8392824, 16777350, 33564672, 67109250, 134234256, 268438860, 536904480, 1073741994, 2147556240, 4294967478, 8590066944

Offset: 1

Author

Michael De Vlieger and N. J. A. Sloane, Mar 15 2019

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3320
• Dennis S. Bernstein, Omran Kouba, Counting Colorful Necklaces and Bracelets in Three Colors, arXiv:1901.10703 [math.CO], 2019.

Crossrefs

Cf. A306888, A306896, A306898.

Programs

Maple

See A306888.

Mathematica

Table[DivisorSum[n, (2^# - (-1)^#) EulerPhi[3 n/#] &], {n, 10^4}] (* Michael De Vlieger, Mar 18 2019 *)

PARI

a(n) = sumdiv(n, d, (2^d - (-1)^d)*eulerphi(3*n/d)); \\ Michel Marcus, Mar 16 2019