%I #13 Jul 30 2019 07:50:00

%S 1,2,3,4,5,6,10,12,14,18,21,22,26,30,42,60,66,78,90,102,114,130,138,

%T 150,170,174,186,210,294,318,330,390,462,510,546,570,690,798,858,870,

%U 930,1050,1110,1218,1230,1290,1410,1470,1554,1590,1722,1770,1830,1974

%N Unitary highly abundant numbers: numbers n such that usigma(n) > usigma(m) for all m < n, where usigma(n) = sum of unitary divisors of n (A034448).

%C Corresponds to A002093 (Highly abundant numbers), with usigma(n) = sum of unitary divisors of n (divisors d such that gcd(d, n/d)=1, A034448) instead of sigma(n) (sum of divisors, A000203).

%C Contains many terms of A280013 (sum of squarefree divisors instead of unitary divisors), but not all of them - the first terms of A280013 that are not in this sequence are 16530, 26070, 8734110, 8757210,...

%H Amiram Eldar, <a href="/A285614/b285614.txt">Table of n, a(n) for n = 1..1000</a>

%e The first 9 values of usigma(n) for n=1..9 are: 1, 3, 4, 5, 6, 12, 8, 9, 10. usigma(10)=18 is higher than these 9 values, thus 10 is in the sequence.

%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; a = {}; k = 0; Do[s = usigma[n]; If[s > k, AppendTo[a, n]; k = s], {n, 1000}]; a

%Y Cf. A034448, A002093, A034683, A129499, A280013.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 22 2017