A302570 - OEIS

A302570

Unitary barely abundant numbers: unitary abundant numbers k such that usigma(k)/k < usigma(m)/m for all unitary abundant numbers m < k, where usigma(k) is the sum of the unitary divisors of k (A034448).

%I #19 Jul 21 2021 00:44:46

%S 30,42,66,70,222,246,258,282,294,318,354,366,402,426,438,474,498,534,

%T 582,606,618,642,654,678,726,750,762,786,822,834,894,906,942,978,1002,

%U 1014,1038,1074,1086,1146,1158,1182,1194,1266,1338,1362,1374,1398,1434

%N Unitary barely abundant numbers: unitary abundant numbers k such that usigma(k)/k < usigma(m)/m for all unitary abundant numbers m < k, where usigma(k) is the sum of the unitary divisors of k (A034448).

%C The unitary version of A071927.

%H Amiram Eldar, <a href="/A302570/b302570.txt">Table of n, a(n) for n = 1..10000</a>

%e The values of usigma(k)/k are 2.4, 2.285..., 2.181..., 2.057..., 2.054...

%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; seq = {}; r = 3; Do[s = usigma[n]/n; If[s > 2 && s < r, AppendTo[seq, n]; r = s], {n, 1, 10000}]; seq

%Y Cf. A034448, A034683, A071927, A302572.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 10 2018