OFFSET
1,4
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wikipedia, Dedekind psi function.
FORMULA
a(n) = A001615(n) - n.
a(n) = Sum_{d|n, d<n} (mu(n/d)^2 * d). - Amiram Eldar, Sep 06 2019
Sum_{k=1..n} a(k) = c * n^2 / 2 + O(n*log(n)), where c = 15/Pi^2 - 1 = 0.519817... . - Amiram Eldar, Dec 08 2023
EXAMPLE
MATHEMATICA
a[1] = 0; a[n_] := n * (Times @@ (1 + 1/FactorInteger[n][[;; , 1]]) - 1); Array[a, 100] (* Amiram Eldar, Sep 06 2019 *)
PROG
(PARI) a(n) = n*(sumdivmult(n, d, issquarefree(d)/d) - 1); \\ Michel Marcus, Mar 18 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Torlach Rush, Mar 16 2019
STATUS
approved