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A293228
a(n) is the sum of proper divisors of n that are squarefree.
6
0, 1, 1, 3, 1, 6, 1, 3, 4, 8, 1, 12, 1, 10, 9, 3, 1, 12, 1, 18, 11, 14, 1, 12, 6, 16, 4, 24, 1, 42, 1, 3, 15, 20, 13, 12, 1, 22, 17, 18, 1, 54, 1, 36, 24, 26, 1, 12, 8, 18, 21, 42, 1, 12, 17, 24, 23, 32, 1, 72, 1, 34, 32, 3, 19, 78, 1, 54, 27, 74, 1, 12, 1, 40, 24, 60, 19, 90, 1, 18, 4, 44, 1, 96, 23, 46, 33, 36, 1, 72, 21, 72, 35, 50, 25, 12, 1, 24
OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{d|n, d<n} A008966(d)*d.
a(n) = A048250(n) - (A008966(n)*n).
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