A306896 a(n) = Sum_{d|n} (2^d + 2*(-1)^d)*phi(n/d).

0, 6, 6, 24, 30, 84, 126, 288, 522, 1080, 2046, 4224, 8190, 16548, 32850, 65856, 131070, 262836, 524286, 1049760, 2097438, 4196412, 8388606, 16782048, 33554550, 67117128, 134218782, 268452240, 536870910, 1073777040, 2147483646, 4295033472, 8589938742, 17180000352, 34359739050

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..3321
• Dennis S. Bernstein, Omran Kouba, Counting Colorful Necklaces and Bracelets in Three Colors, arXiv:1901.10703 [math.CO], 2019.

Crossrefs

Cf. A306888, A306897.

Programs

Maple

See A306888.

Mathematica

Table[DivisorSum[n, (2^# + 2 (-1)^#) EulerPhi[n/#] &], {n, 35}] (* Michael De Vlieger, Mar 18 2019 *)

PARI

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