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%I #12 Jul 29 2020 20:39:27
%S 1,2,6,30,210,2310,110670,182910,898590,22851570,26266170,45255210,
%T 64124970,265402410,1374105810,1631268870
%N Unitary barely 3-deficient numbers: numbers m such that usigma(k)/k < usigma(m)/m < 3 for all numbers k < m, where usigma is the sum of unitary divisors function (A034448).
%C Unitary 3-deficient numbers are numbers k such that usigma(k) < 3*k, i.e., numbers that are not in A285615.
%C The corresponding values of usigma(m)/m are 1, 1.5, 2, 2.4, 2.742..., 2.992..., ...
%C Are terms squarefree? At some point, do we know that a(n) is divisible by primorial(k) for all n > N(k) for some N(k)? - _David A. Corneth_, Jul 29 2020
%C Not all the terms are squarefree. E.g., a(12) = 45255210 is divisible by 11^2.
%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); s = {}; rm = 0; Do[r = usigma[n]/n; If[r < 3 && r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^5}]; s
%Y The unitary version of A307122.
%Y Cf. A034448, A129487, A285615, A302572, A336671.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jul 29 2020
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