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%I #15 May 12 2020 16:06:04
%S 30,42,66,70,78,102,114,138,150,174,186,222,246,258,282,294,318,354,
%T 366,402,420,426,438,474,498,534,582,606,618,630,642,654,660,678,726,
%U 750,762,780,786,822,834,840,894,906,942,978,990,1002,1014,1020,1038,1074,1086
%N Unitary admirable numbers: numbers k such that there is a proper unitary divisor d of k such that usigma(k) - 2d = 2k, where usigma is the sum of unitary divisors function (A034448).
%C Differs from A302574(n) at n >= 30.
%C Equivalently, numbers that equal to the sum of their proper unitary divisors, with one of them taken with a minus sign.
%C The unitary version of A111592.
%C The squarefree terms are also admirable numbers (A111592). The nonsquarefree terms are 150, 294, 420, 630, 660, 726, 750, 780, 840, 990, ...
%C The unitary abundant numbers (A034683) that are not unitary admirable numbers are: 210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 924, 930, 966, ...
%H Amiram Eldar, <a href="/A328328/b328328.txt">Table of n, a(n) for n = 1..10000</a>
%e 150 is in the sequence since 150 = 1 + 2 + 3 - 6 + 25 + 50 + 75 is the sum of its proper unitary divisors with one of them, 6, taken with a minus sign.
%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); aQ[n_] := (ab = usigma[n] - 2n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && CoprimeQ[2*n/ab, ab/2]; Select[Range[1086], aQ]
%Y Cf. A034448, A077610, A111592, A302574.
%Y Subsequence of A034683 and A290466.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 12 2019
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