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 A380848 #12 Feb 12 2025 03:16:38
%S A380848 123832800,247695840,268337160,495421920,536707080,990874080,
%T A380848 1073446920,1981778400,2146926600,3963587040,4293885960,7927204320,
%U A380848 8587804680,15854438880,17175642120,31708908000,34351317000,63417846240,68702666760,124884879840,126713795040,126835722720
%N A380848 Numbers k such that A380845(k) = 4*k.
%C A380848 Analogous to 4-perfect numbers (A027687) with A380845 instead of A000203.
%C A380848 All the terms are 4-abundant numbers (A068404), because A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).
%C A380848 Are there numbers k such that A380845(k) = m*k for integers m >= 5? There are none below 1.6*10^11.
%t A380848 q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 4*k]; Select[Range[3*10^8], q]
%o A380848 (PARI) isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 4*k;}
%Y A380848 Cf. A000203, A005100, A027687, A380845, A380846, A380847.
%Y A380848 Subsequence of A068404.
%K A380848 nonn,base
%O A380848 1,1
%A A380848 _Amiram Eldar_, Feb 05 2025
%E A380848 a(19)-a(22) from _Jinyuan Wang_, Feb 12 2025