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A381070 Numbers k such that A380845(k)/k > A380845(m)/m for all m < k.

%I A381070 #7 Feb 17 2025 03:28:49
%S A381070 1,2,4,8,16,18,36,72,144,288,540,1080,2160,4320,8640,17280,34560,
%T A381070 45360,68040,90720,106680,136080,213360,272160,320040,640080,1280160,
%U A381070 2560320,2577960,5155920,10311840,15467760,30935520,61871040,123742080,247484160,494968320,681080400
%N A381070 Numbers k such that A380845(k)/k > A380845(m)/m for all m < k.
%C A381070 Analogous to superabundant numbers (A004394) with A380845 instead of A000203.
%C A381070 The least number k for which A380845(k)/k >= 2 is k = a(6) = A380846(1) = 18.
%C A381070 The least number k for which A380845(k)/k >= 3 is k = a(12) = A380930(1) = 1080.
%C A381070 The least number k for which A380845(k)/k >= 4 is k = a(30) = A380931(1) = 5155920.
%C A381070 It seems that A380845(k)/k is unbounded (see the plot in the links section). What is the least number k for which A380845(k)/k >= 5?
%H A381070 Amiram Eldar, <a href="/A381070/b381070.txt">Table of n, a(n) for n = 1..46</a>
%H A381070 Amiram Eldar, <a href="/A381070/a381070.jpg">Plot of A380845(n)/n at indices of record</a>.
%t A381070 r[n_] := Module[{h = DigitCount[n, 2, 1]}, DivisorSum[n, # &, DigitCount[#, 2, 1] == h &]/n]; seq[lim_] := Module[{s = {}, rm = 0, r1}, Do[r1 = r[k]; If[r1 > rm, rm = r1; AppendTo[s, k]], {k, 1, lim}]; s]; seq[10^5]
%o A381070 (PARI) r(n) = {my(h = hammingweight(n)); sumdiv(n, d, d * (hammingweight(d) == h)) / n;}
%o A381070 list(lim) = {my(rm = 0, r1); for(k = 1, lim, r1 = r(k); if(r1 > rm, rm = r1; print1(k, ", "))); }
%Y A381070 Cf. A000203, A004394, A380845, A380846, A380929, A380930, A380931, A381069.
%K A381070 nonn,base
%O A381070 1,2
%A A381070 _Amiram Eldar_, Feb 13 2025