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Total distance from n to each of its refactorable unitary divisors.
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%I #3 May 27 2023 13:30:21

%S 0,1,2,3,4,9,6,7,8,17,10,11,12,25,14,15,16,42,18,19,20,41,22,39,24,49,

%T 26,27,28,57,30,31,32,65,34,62,36,73,38,71,40,81,42,43,80,89,46,47,48,

%U 97,50,51,52,105,54,103,56,113,58,107,60,121,116,63,64,129,66,67,68,137,70

%N Total distance from n to each of its refactorable unitary divisors.

%F a(n) = Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} (n - d).

%F a(n) = n * A363298(n) - A363085(n).

%t a[n_] := DivisorSum[n, n - # &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]

%Y Cf. A363085, A363298.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, May 27 2023