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A321322 a(n) = Sum_{d|n} mu(n/d)*J_2(d), where J_2() is the Jordan function (A007434). 1
1, 2, 7, 9, 23, 14, 47, 36, 64, 46, 119, 63, 167, 94, 161, 144, 287, 128, 359, 207, 329, 238, 527, 252, 576, 334, 576, 423, 839, 322, 959, 576, 833, 574, 1081, 576, 1367, 718, 1169, 828, 1679, 658, 1847, 1071, 1472, 1054, 2207, 1008, 2304, 1152, 2009, 1503, 2807, 1152, 2737 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Möbius transform applied twice to squares.

LINKS

Table of n, a(n) for n=1..55.

N. J. A. Sloane, Transforms

FORMULA

G.f.: Sum_{k>=1} A007427(k)*x^k*(1 + x^k)/(1 - x^k)^3.

a(n) = Sum_{d|n} mu(n/d)*phi(d)*psi(d), where phi() is the Euler totient function (A000010) and psi() is the Dedekind psi function (A001615).

MATHEMATICA

Table[Sum[MoebiusMu[n/d] Sum[MoebiusMu[d/j] j^2, {j, Divisors[d]}], {d, Divisors[n]}], {n, 55}]

nmax = 55; Rest[CoefficientList[Series[Sum[DivisorSum[k, MoebiusMu[#] MoebiusMu[k/#] &] x^k (1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]]

CROSSREFS

Cf. A000010, A001615, A007427, A007431, A007433, A007434, A008683.

Sequence in context: A293646 A020895 A174247 * A065139 A093916 A042451

Adjacent sequences:  A321319 A321320 A321321 * A321323 A321324 A321325

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Nov 04 2018

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)