OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{d|n, d<n} A008966(d).
G.f.: Sum_{k>=1} mu(k)^2*x^(2*k)/(1 - x^k). - Ilya Gutkovskiy, Oct 28 2018
Sum_{k=1..n} a(k) ~ (6/Pi^2)*n*(log(n) + 2*(gamma - 1 - zeta'(2)/zeta(2))), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 01 2023
MAPLE
with(numtheory): seq(coeff(series(add(mobius(k)^2*x^(2*k)/(1-x^k), k=1..n), x, n+1), x, n), n = 1 .. 120); # Muniru A Asiru, Oct 28 2018
MATHEMATICA
Table[Count[Most[Divisors[n]], _?SquareFreeQ], {n, 110}] (* Harvey P. Dale, Jun 15 2021 *)
a[n_] := 2^PrimeNu[n] - Boole[SquareFreeQ[n]]; Array[a, 100] (* Amiram Eldar, Jun 30 2022 *)
PROG
(PARI) A293227(n) = sumdiv(n, d, (d<n)*issquarefree(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2017
STATUS
approved