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Nonunitary superabundant numbers: numbers m such that nusigma(m)/m > nusigma(k)/k for all k < m, where nusigma(m) is the sum of nonunitary divisors of m (A048146).
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%I #7 Nov 23 2019 23:14:00

%S 1,4,8,16,24,36,48,72,144,288,360,432,720,1440,1800,2160,3600,7200,

%T 10800,15120,21600,25200,50400,75600,151200,302400,453600,529200,

%U 831600,1058400,1663200,2116800,3175200,3326400,4989600,5821200,9979200,11642400,21621600

%N Nonunitary superabundant numbers: numbers m such that nusigma(m)/m > nusigma(k)/k for all k < m, where nusigma(m) is the sum of nonunitary divisors of m (A048146).

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; rm = -1; s = {}; Do[r = nusigma[n]/n; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 10000}]; s

%Y The nonunitary version of A004394.

%Y Cf. A034448, A048146, A064597, A309141.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 23 2019