This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A293453 #20 Oct 01 2020 03:02:22
%S A293453 6,24,28,42,54,56,60,78,84,88,96,102,108,114,120,126,132,140,150,168,
%T A293453 174,176,186,198,204,216,220,222,224,228,240,246,252,258,260,264,270,
%U A293453 276,280,294,308,312,330,336,340,342,348,350,352,354,366,368,372,378,380,384,390,396,402
%N A293453 Zumkeller numbers k such that sigma(k)/2 is a Zumkeller number.
%C A293453 Subsequence of A083207 (Zumkeller numbers).
%C A293453 Conjecture: Any four consecutive Zumkeller numbers include at least one term of the present sequence (verified for the first 10^5 Zumkeller numbers).
%C A293453 The perfect numbers (A000396) are all trivially in this sequence.
%H A293453 Amiram Eldar, <a href="/A293453/b293453.txt">Table of n, a(n) for n = 1..10000</a>
%e A293453 The fourth Zumkeller number is 24, since sigma(24) = A000203(24) = 60, 60/2 = 30, and the divisors of 24 can be partitioned as 1 + 2 + 3 + 4 + 8 + 12 = 6 + 24 = 30.
%e A293453 In turn, 30 is also a Zumkeller number, as sigma(30)/2 = 72/2 = 36 and 1 + 2 + 3 + 5 + 10 + 15 = 6 + 30 = 36.
%e A293453 Therefore 24 is in this sequence.
%e A293453 But since 36 is not a Zumkeller number at all, 30 is not in this sequence.
%t A293453 zumkellerQ[n_] := Module[{d = Divisors[n], t, ds, x}, ds = Plus@@d; If[Mod[ds, 2] > 0, False, t = CoefficientList[Product[1 + x^i, {i, d}], x]; t[[1 + ds/2]] > 0]]; zn = Select[Range[1000], zumkellerQ] (* a code by _T. D. Noe_ at A083207 *); Select[zn, zumkellerQ[DivisorSigma[1, #]/2] &]
%Y A293453 Cf. A000203, A000396, A083207.
%K A293453 easy,nonn
%O A293453 1,1
%A A293453 _Ivan N. Ianakiev_, Oct 09 2017