OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} A000005(d)*d^2.
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
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