A306898 a(n) = Sum_{d|n} 2^d*phi(2*n/d).

2, 8, 12, 32, 40, 96, 140, 320, 540, 1120, 2068, 4320, 8216, 16688, 32880, 66176, 131104, 263376, 524324, 1050880, 2097480, 4198480, 8388652, 16786368, 33554600, 67125344, 134218836, 268468928, 536870968, 1073809920, 2147483708, 4295099648, 8589938808, 17180131456, 34359739120, 68720011776

Offset

1,1

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.

Formula

a(n) = 2 * n * A000013(n). - Seiichi Manyama, Jul 14 2023

Maple

See A306888.

Mathematica

Table[DivisorSum[n, 2^# *EulerPhi[2 n/#] &], {n, 36}] (* Michael De Vlieger, Mar 18 2019 *)

Prog

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

Crossrefs

Cf. A000013, A306888, A306896, A306905.

Sequence in context: A047174 A048074 A126775 * A069185 A037197 A125712

Adjacent sequences: A306895 A306896 A306897 * A306899 A306900 A306901

Keyword

nonn

Author

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

Status

approved