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A360429
Inverse Mobius transformation of A034714.
1
1, 9, 19, 57, 51, 171, 99, 313, 262, 459, 243, 1083, 339, 891, 969, 1593, 579, 2358, 723, 2907, 1881, 2187, 1059, 5947, 1926, 3051, 3178, 5643, 1683, 8721, 1923, 7737, 4617, 5211, 5049, 14934, 2739, 6507, 6441, 15963, 3363, 16929, 3699, 13851, 13362, 9531, 4419, 30267, 7302, 17334
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} A000005(d)*d^2.
Dirichlet convolution of A034714 and A000012.
Dirichlet g.f.: zeta^2(s-2)*zeta(s).
From Amiram Eldar, Feb 09 2023: (Start)
Multiplicative with a(p^e) = ((e+1)*p^(2*e+4) - (e+2)*p^(2*e+2) + 1)/(p^2-1)^2.
Sum_{k=1..n} a(k) ~ (log(n) + 2*gamma - 1/3 + zeta'(3)/zeta(3)) * n^3 * zeta(3)/3, where gamma is Euler's constant (A001620). (End)
MAPLE
A360429 := proc(n)
add(numtheory[tau](d)*d^2, d=numtheory[divisors](n)) ;
end proc:
MATHEMATICA
f[p_, e_] := ((e+1)*p^(2*e+4) - (e+2)*p^(2*e+2) + 1)/(p^2-1)^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 09 2023 *)
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
R. J. Mathar, Feb 07 2023
STATUS
approved