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%I #15 Sep 22 2019 07:48:07
%S 24,30,84,120,140,224,234,270,308,364,476,532,644,672,1488,1638,2480,
%T 3472,3724,4095,5456,5624,6200,6435,6448,8432,9424,11408,14384,15872,
%U 18352,20336,21328,23312,24384,26288,29264,29450,30256,33232,35150
%N Admirable numbers n such that the subtracted divisor is > sqrt(n).
%C Solutions to sigma(x)=2(x+d) with d > sqrt(x) being a proper divisor of x. The subsequence A165772 contains most of the terms. - _M. F. Hasler_, Oct 11 2009
%H Amiram Eldar, <a href="/A109321/b109321.txt">Table of n, a(n) for n = 1..1200</a>
%e a(2)=30 because 1+2+3+5+10+15-6 = 30 and 6 > sqrt(30) = 5.477...
%t aQ[n_] := (d = DivisorSigma[1, n] - 2n) > 0 && EvenQ[d] && Mod[n, d/2] == 0 && d < 2n && d^2 > 4n; Select[Range[35150], aQ] (* _Amiram Eldar_, Sep 22 2019 *)
%o (PARI) is_A109321(n)= my(d=sigma(n)-2*n); d>0 && bittest(d,0)==0 && d<2*n && d*d>4*n && 2*n%d==0 \\ _M. F. Hasler_, Oct 11 2009
%Y Cf. A111592.
%K nonn
%O 1,1
%A _Jason Earls_, Aug 20 2005
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