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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).
5

%I #9 Jan 12 2024 01:28:22

%S 1,4,8,12,16,24,32,36,48,64,72,96,108,120,144,180,192,216,288,360,432,

%T 504,576,648,720,864,1008,1080,1296,1440,1728,1800,2016,2160,2520,

%U 2880,3024,3240,3456,3528,3600,4320,5040,5400,5760,6048,6480,7056,7200,8640

%N 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).

%C 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, ...

%H Amiram Eldar, <a href="/A329883/b329883.txt">Table of n, a(n) for n = 1..500</a>

%t 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

%Y The nonunitary version of A002093.

%Y Cf. A048146, A064597, A309141, A329882.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 23 2019