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A293228 a(n) is the sum of proper divisors of n that are squarefree. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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

PROG

(PARI) A293228(n) = sumdiv(n, d, (d<n)*issquarefree(d)*d);

CROSSREFS

Cf. A005117, A008966, A048250, A293227, A293235.

Sequence in context: A115364 A016476 A293436 * A169814 A068436 A019570

Adjacent sequences:  A293225 A293226 A293227 * A293229 A293230 A293231

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 08 2017

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)