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%I #9 Oct 27 2019 11:11:49
%S 12,20,24,30,40,42,54,70,102,114,120,222,270,402,1002,2022,2202,10002,
%T 10014,10792,11202,12102,21102,31002,32128,45356,103002,110202,111102,
%U 128768,740870,1000002,1000014,1001202,1002102,1021002,1111002,1200102
%N Admirable Harshad numbers such that the subtracted divisor is also a Harshad number.
%H Amiram Eldar, <a href="/A109396/b109396.txt">Table of n, a(n) for n = 1..100</a>
%e 12 is in the sequence since it is a Harshad number (1 + 2 = 3 is a divisor of 12), an admirable number: 1 - 2 + 3 + 4 + 6 = 12, and the subtracted divisor, 2, is also a Harshad number.
%t hQ[n_] := Divisible[n, Plus @@ IntegerDigits@n]; aQ[n_] := hQ[n] && (d = DivisorSigma[1, n] - 2*n) > 0 && EvenQ[d] && d/2 < n && hQ[d/2] && Divisible[n, d/2]; Select[Range[50000], aQ] (* _Amiram Eldar_, Oct 27 2019 *)
%Y Cf. A111592, A005349, A111947, A111948.
%K base,nonn
%O 1,1
%A _Jason Earls_, Aug 26 2005
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