A329882 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).

1, 4, 8, 16, 24, 36, 48, 72, 144, 288, 360, 432, 720, 1440, 1800, 2160, 3600, 7200, 10800, 15120, 21600, 25200, 50400, 75600, 151200, 302400, 453600, 529200, 831600, 1058400, 1663200, 2116800, 3175200, 3326400, 4989600, 5821200, 9979200, 11642400, 21621600

Offset: 1

Author

Amiram Eldar, Nov 23 2019

Keywords

• nonn

Crossrefs

The nonunitary version of A004394.

Cf. A034448, A048146, A064597, A309141.

Programs

Mathematica

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