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Sum of the divisor complements of the unitary squarefree divisors of n.
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%I #10 May 26 2023 12:29:07

%S 1,3,4,4,6,12,8,8,9,18,12,16,14,24,24,16,18,27,20,24,32,36,24,32,25,

%T 42,27,32,30,72,32,32,48,54,48,36,38,60,56,48,42,96,44,48,54,72,48,64,

%U 49,75,72,56,54,81,72,64,80,90,60,96,62,96,72,64,84,144,68,72,96,144,72

%N Sum of the divisor complements of the unitary squarefree divisors of n.

%F a(n) = n * Sum_{d|n, gcd(d,n/d)=1} mu(d)^2 / d.

%t a[n_] := DivisorSum[n, n/# &, CoprimeQ[#, n/#] && SquareFreeQ[#] &]; Array[a, 100] (* _Amiram Eldar_, May 26 2023 *)

%o (PARI) a(n) = sumdiv(n, d, if ((gcd(d, n/d) == 1) && issquarefree(d), n/d)); \\ _Michel Marcus_, May 26 2023

%Y Cf. A092261.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, May 26 2023