A329883 Nonunitary highly abundant numbers: numbers m such that nusigma(m) > nusigma(k) for all k < m, where s(n) is the sum of nonunitary divisors of n (A048146).

1, 4, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 108, 120, 144, 180, 192, 216, 288, 360, 432, 504, 576, 648, 720, 864, 1008, 1080, 1296, 1440, 1728, 1800, 2016, 2160, 2520, 2880, 3024, 3240, 3456, 3528, 3600, 4320, 5040, 5400, 5760, 6048, 6480, 7056, 7200, 8640

Offset: 1

Author

Amiram Eldar, Nov 23 2019

Keywords

• nonn

Comments

The corresponding record values are 0, 2, 6, 8, 14, 24, 30, 41, 56, 62, 105, 120, 140, 144, 233, 246, 248, 348, 489, 630, 764, 840, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

The nonunitary version of A002093.

Cf. A048146, A064597, A309141, A329882.

Programs

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; num = -1; s = {}; Do[nu = nusigma[n]; If[nu > num, num = nu; AppendTo[s, n]], {n, 1, 10^4}]; s