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 A293227 a(n) is the number of proper divisors of n that are squarefree. 3

%I

%S 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,

%T 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,

%U 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

%N a(n) is the number of proper divisors of n that are squarefree.

%H Antti Karttunen, <a href="/A293227/b293227.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

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

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

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

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

%p 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

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

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 08 2017

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Last modified February 27 09:44 EST 2020. Contains 332301 sequences. (Running on oeis4.)