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 A380846 #14 Feb 10 2025 16:10:06
%S A380846 18,42,90,186,196,306,378,420,534,618,654,690,762,834,868,906,1062,
%T A380846 1110,1194,1242,1326,1362,1422,1458,1530,1698,1764,1818,1866,2118,
%U A380846 2214,2262,2324,2346,2490,2598,2670,2706,2730,2778,2838,2862,2884,2922,2958,2994,3066,3138
%N A380846 Numbers k such that A380845(k) = 2*k.
%C A380846 Analogous to perfect numbers (A000396) with A380845 instead of A000203.
%C A380846 All the terms are abundant numbers (A005101), since A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).
%C A380846 Are there odd terms in this sequence? There are none below 10^11.
%H A380846 Amiram Eldar, <a href="/A380846/b380846.txt">Table of n, a(n) for n = 1..10000</a>
%e A380846 18 is a term since A380845(18) = 36 = 2 * 18.
%t A380846 q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 2*k]; Select[Range[3200], q]
%o A380846 (PARI) isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 2*k;}
%Y A380846 Cf. A000203, A000396, A005100, A380845, A380847, A380848.
%Y A380846 Subsequence of A005101.
%K A380846 nonn,base,easy
%O A380846 1,1
%A A380846 _Amiram Eldar_, Feb 05 2025