OFFSET
1,3
LINKS
FORMULA
a(n) = (1/n) * Sum_{d|n} mu(n/d)*n^d.
Asymptotic to n^(n-1) = A000169(n).
a(n) is the n-th term of the inverse Euler transform of j-> n^j. - Alois P. Heinz, Jun 23 2018
a(n) = [x^n] Sum_{k>=1} mu(k)*log(1/(1 - n*x^k))/k. - Ilya Gutkovskiy, May 20 2019
MAPLE
with(numtheory):
a:= n-> add(n^d *mobius(n/d), d=divisors(n))/n:
seq(a(n), n=1..25); # Alois P. Heinz, Dec 21 2014
MATHEMATICA
Table[Total@Map[ MoebiusMu[#1] n^(n/#1 - 1) &, Divisors[n]], {n, 20}] (* Olivier Gérard, Aug 05 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Sep 04 2002
STATUS
approved