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A293227 a(n) is the number of proper divisors of n that are squarefree. 3
0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 2, 4, 1, 7, 1, 2, 3, 3, 3, 4, 1, 3, 3, 4, 1, 7, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 8, 1, 3, 4, 2, 3, 7, 1, 4, 3, 7, 1, 4, 1, 3, 4, 4, 3, 7, 1, 4, 2, 3, 1, 8, 3, 3, 3, 4, 1, 8, 3, 4, 3, 3, 3, 4, 1, 4, 4, 4, 1, 7, 1, 4, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = Sum_{d|n, d<n} A008966(d).

a(n) = A034444(n) - A008966(n).

a(n) = 2^A001221(n) - A008683(n)^2 = 2^omega(n) - mu(n)^2.

G.f.: Sum_{k>=1} mu(k)^2*x^(2*k)/(1 - x^k). - Ilya Gutkovskiy, Oct 28 2018

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

PROG

(PARI) A293227(n) = sumdiv(n, d, (d<n)*issquarefree(d));

CROSSREFS

Cf. A001221, A005117, A008683, A008966, A034444, A293228, A293234.

Sequence in context: A303757 A323014 A182850 * A291208 A241165 A233183

Adjacent sequences:  A293224 A293225 A293226 * A293228 A293229 A293230

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 08 2017

STATUS

approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)