A346758 a(n) = Sum_{d|n} mu(n/d) * floor(d^2/4).

0, 1, 2, 3, 6, 6, 12, 12, 18, 18, 30, 24, 42, 36, 48, 48, 72, 54, 90, 72, 96, 90, 132, 96, 150, 126, 162, 144, 210, 144, 240, 192, 240, 216, 288, 216, 342, 270, 336, 288, 420, 288, 462, 360, 432, 396, 552, 384, 588, 450, 576, 504, 702, 486, 720, 576, 720, 630, 870, 576, 930

Offset

1,3

Comments

Moebius transform of quarter-squares (A002620).

Links

Table of n, a(n) for n=1..61.

Formula

G.f.: Sum_{k>=1} mu(k) * x^(2*k) / ((1 + x^k) * (1 - x^k)^3).

a(n) = J_2(n) / 4 for n >= 3, where J_() is the Jordan function.

Mathematica

Table[Sum[MoebiusMu[n/d] Floor[d^2/4], {d, Divisors[n]}], {n, 1, 61}]
nmax = 61; CoefficientList[Series[Sum[MoebiusMu[k] x^(2 k)/((1 + x^k) (1 - x^k)^3), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(d^2\4)); \\ Michel Marcus, Aug 03 2021

Crossrefs

Cf. A002620, A007434, A023022, A346759.

Sequence in context: A119319 A069808 A131259 * A143177 A129648 A129649

Adjacent sequences: A346755 A346756 A346757 * A346759 A346760 A346761

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved