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A360428
Inverse Mobius transformation of A338164.
7
1, 7, 17, 40, 49, 119, 97, 208, 225, 343, 241, 680, 337, 679, 833, 1024, 577, 1575, 721, 1960, 1649, 1687, 1057, 3536, 1825, 2359, 2673, 3880, 1681, 5831, 1921, 4864, 4097, 4039, 4753, 9000, 2737, 5047, 5729, 10192, 3361, 11543, 3697, 9640, 11025, 7399, 4417, 17408, 7105, 12775
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} A008683(n/d)*A000005(d)*d^2.
Dirichlet convolution of A034714 and A008683.
Dirichlet g.f.: zeta^2(s-2)/zeta(s).
From Amiram Eldar, Feb 09 2023: (Start)
Multiplicative with a(p^e) = (e + 1 - e/p^2)*p^(2*e).
Sum_{k=1..n} a(k) ~ (log(n) + 2*gamma - 1/3 - zeta'(3)/zeta(3)) * n^3 / (3*zeta(3)), where gamma is Euler's constant (A001620). (End)
From Peter Bala, Jan 16 2024: (Start)
a(n) = Sum_{1 <= i, j <= n} gcd(i, j, n)^2. Cf. A069097.
a(n) = Sum_{d divides n} d^2 * J_2(n/d), where J_2(n) = A007434(n). (End)
MAPLE
A360428 := proc(n)
add(numtheory[mobius](n/d)*numtheory[tau](d)*d^2, d=numtheory[divisors](n)) ;
end proc:
MATHEMATICA
f[p_, e_] := (e + 1 - e/p^2)*p^(2*e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 09 2023 *)
KEYWORD
nonn,mult,easy
AUTHOR
R. J. Mathar, Feb 07 2023
STATUS
approved