OFFSET
1,4
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
a(n) = Sum_{d|n, d<n} A008966(d)*d.
G.f.: Sum_{k>=1} mu(k)^2*k*x^(2*k)/(1 - x^k). - Ilya Gutkovskiy, Oct 28 2018
From Amiram Eldar, Oct 09 2022: (Start)
a(n) = 1 iff n is a prime.
a(n) = 3 iff n is a power of 2 greater than 2 (A020707).
Sum_{k=1..n} a(k) ~ (1/2 - 3/Pi^2) * n^2. (End)
MAPLE
with(numtheory): seq(coeff(series(add(mobius(k)^2*k*x^(2*k)/(1-x^k), k=1..n), x, n+1), x, n), n = 1 .. 120); # Muniru A Asiru, Oct 28 2018
MATHEMATICA
a[n_] := Times @@ (1 + (f = FactorInteger[n])[[;; , 1]]) - If[AllTrue[f[[;; , 2]], # == 1 &], n, 0]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Oct 09 2022 *)
PROG
(PARI) A293228(n) = sumdiv(n, d, (d<n)*issquarefree(d)*d);
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2017
STATUS
approved