OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} mu(d)^2 * sigma(d).
Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/(12*zeta(3)) = 0.684216... (A335005). - Amiram Eldar, Nov 13 2022
MATHEMATICA
a[1] = 1; a[n_] := Times @@ ((#[[1]] + 2) & /@ FactorInteger[n]); Table[a[n], {n, 70}]
nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k]^2 DivisorSigma[1, k] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, moebius(d)^2 * sigma(d)) \\ Andrew Howroyd, Apr 15 2021
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Apr 15 2021
STATUS
approved