cp's OEIS Frontend

A329189 3-admirable numbers: 3-abundant numbers (A068403) k such that exists a proper divisor d of k such that sigma(k) - 2*d = 3*k, where sigma(k) is the sum of divisors of k (A000203).

%I A329189 #15 Nov 08 2019 03:16:39
%S A329189 180,240,360,420,504,540,600,780,1080,1344,1872,1890,2016,2184,2352,
%T A329189 2376,2688,3192,3276,3744,4284,4320,4680,5292,5376,5796,6048,6552,
%U A329189 7128,7344,7440,8190,9504,10296,10416,13776,14850,18600,19824,19872,20496,21528,22932
%N A329189 3-admirable numbers: 3-abundant numbers (A068403) k such that exists a proper divisor d of k such that sigma(k) - 2*d = 3*k, where sigma(k) is the sum of divisors of k (A000203).
%C A329189 Analogous to admirable numbers (A111592) as 3-perfect numbers (A005820) are analogous to perfect numbers (A000396).
%C A329189 The proper divisors of each term k can be added to a sum of 2*k with one divisor taken with a minus sign.
%H A329189 Amiram Eldar, <a href="/A329189/b329189.txt">Table of n, a(n) for n = 1..810</a> (terms below 10^11)
%e A329189 180 is a term since its proper divisors can be added to 1 + 2 - 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 = 360 = 2 * 180, with one divisor, 3, taken with a minus sign.
%t A329189 aQ[n_] := (ab = DivisorSigma[1, n] - 3 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2]; Select[Range[23000], aQ]
%Y A329189 Cf. A000203, A000396, A068403, A111592.
%K A329189 nonn
%O A329189 1,1
%A A329189 _Amiram Eldar_, Nov 07 2019