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 A332712 a(n) = Sum_{d|n} mu(d/gcd(d, n/d)). 2
 1, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Dirichlet g.f.: zeta(2*s)^2 * zeta(3*s) / zeta(6*s). a(n) = Sum_{d|n} mu(lcm(d, n/d)/d). a(n) = Sum_{d|n} (-1)^bigomega(n/d) * A005361(d). a(n) = Sum_{d|n} A010052(n/d) * A112526(d). Sum_{k=1..n} a(k) ~ zeta(3/2)*sqrt(n)*log(n)/(2*zeta(3)) + ((2*gamma - 1)*zeta(3/2) + 3*zeta'(3/2)/2 - 3*zeta(3/2)*zeta'(3)/zeta(3)) * sqrt(n)/zeta(3) + 6*zeta(2/3)^2 * n^(1/3)/Pi^2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 21 2020 Multiplicative with a(p^e) = A028242(e). - Amiram Eldar, Nov 30 2020 MATHEMATICA Table[Sum[MoebiusMu[d/GCD[d, n/d]], {d, Divisors[n]}], {n, 1, 100}] A005361[n_] := Times @@ (#[[2]] & /@ FactorInteger[n]); a[n_] := Sum[(-1)^PrimeOmega[n/d] A005361[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}] f[p_, e_] := 3*Floor[e/2] - e + 1; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Nov 30 2020 *) PROG (PARI) a(n) = sumdiv(n, d, moebius(d/gcd(d, n/d))); \\ Michel Marcus, Feb 20 2020 CROSSREFS Cf. A001222, A001694 (positions of nonzero terms), A005361, A007427, A008683, A008836, A028242, A052485 (positions of 0's), A062838 (positions of 1's), A112526, A252505, A322483, A332685, A332713. Sequence in context: A035699 A132406 A197881 * A079126 A339086 A186336 Adjacent sequences:  A332709 A332710 A332711 * A332713 A332714 A332715 KEYWORD nonn,mult AUTHOR Ilya Gutkovskiy, Feb 20 2020 STATUS approved

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)