OFFSET
1,2
LINKS
N. J. A. Sloane, Transforms.
FORMULA
a(n) = Sum_{d|n} sigma_d(d) * mu(n/d).
EXAMPLE
a(6) = 47418; a(6) = Sum_{d|6} sigma_d(d) * mu(6/d) = sigma_1(1) * mu(6/1) + sigma_2(2) * mu(6/2) + sigma_3(3) * mu(6/3) + sigma_6(6) * mu(6/6) = 1*1 + 5*(-1) + 28*(-1) + 47450*1 = 47418.
MATHEMATICA
a[n_] := DivisorSum[n, DivisorSigma[#, #]*MoebiusMu[n/#] &]; Array[a, 20] (* Wesley Ivan Hurt, Nov 12 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, sigma(d, d)*moebius(n/d)); \\ Michel Marcus, Jun 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 24 2022
STATUS
approved