cp's OEIS Frontend

A381069 Numbers k that have a record number of divisors that have the same binary weight as k.

%I A381069 #8 Feb 17 2025 03:28:41
%S A381069 1,2,4,8,16,32,64,72,144,288,576,1080,2160,4320,8640,17280,34560,
%T A381069 69120,99360,136080,198720,272160,397440,529200,544320,1058400,
%U A381069 2116800,3160080,4233600,6320160,8467200,12640320,16934400,25280640,50561280,76744800,101122560,102816000
%N A381069 Numbers k that have a record number of divisors that have the same binary weight as k.
%C A381069 Indices of records of A380844, i.e., numbers k such that A380844(k) > A380844(m) for all m < k.
%C A381069 This sequence is infinite since A380844 is unbounded (e.g., A380844(2^n) = n+1).
%C A381069 Analogous to highly composite numbers (A002182) with the number of divisors with the same binary weight (A380844) instead of the number of divisors (A000005).
%C A381069 The corresponding record values are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 20, 24, 28, ... (see the link for more values).
%H A381069 Amiram Eldar, <a href="/A381069/b381069.txt">Table of n, a(n) for n = 1..60</a>
%H A381069 Amiram Eldar, <a href="/A381069/a381069.txt">Table of n, a(n), A380844(a(n)) for n = 1..60</a>
%t A381069 seq[lim_] := Module[{h, d, dmax = 0, s = {}}, Do[h = DigitCount[k, 2, 1]; d = DivisorSum[k, 1 &, DigitCount[#, 2, 1] == h &]; If[d > dmax, dmax = d; AppendTo[s, k]], {k, 1, lim}]; s]; seq[10^5]
%o A381069 (PARI) list(lim) = {my(h, d, dmax = 0); for(k = 1, lim, h = hammingweight(k); d = sumdiv(k, d, hammingweight(d) == h); if(d > dmax, dmax = d; print1(k, ", ")));}
%Y A381069 Cf. A000005, A002182, A380844, A381070.
%K A381069 nonn,base
%O A381069 1,2
%A A381069 _Amiram Eldar_, Feb 12 2025