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 A359082 #13 Mar 13 2023 09:55:05
%S A359082 1,3,15,63,255,495,4095,96255,98175,130815,203775,1048575,5810175,
%T A359082 6455295,16777215,67096575,88062975,389656575,553517055,850917375,
%U A359082 1157349375,9141354495,12826279935,22828220415,26818379775,31684427775,68719476735,242870910975,1168231038975
%N A359082 Indices of records in A246600.
%C A359082 Numbers k with a record number of divisors d such that the bitwise OR of k and d is equal to k (or equivalently, the bitwise AND of k and d is equal to d).
%C A359082 All the terms are odd since A246600(2*k) = A246600(k).
%C A359082 This sequence is infinite since A246600(2^m-1) = A000005(2^m-1) = A046801(m), and A046801 is unbounded (A046801(2^(m+1)) > A046801(2^m) for all m >= 0).
%C A359082 The corresponding record values are 1, 2, 4, 6, 8, 11, 24, 25, 28, 32, 35, 48, 56, 89, 96, 105, 121, 127, 148, 162, 216, 243, 245, 256, 319, 358, 512, 633, 768, ... .
%C A359082 2*10^11 < a(28) <= 2^48 - 1.
%H A359082 Martin Ehrenstein, <a href="/A359082/b359082.txt">Table of n, a(n) for n = 1..36</a>
%H A359082 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A359082 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.
%t A359082 s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; seq={}; sm = 0; Do[If[(sn = s[n]) > sm, sm = sn; AppendTo[seq, n]], {n, 1, 10^6}]; seq
%o A359082 (PARI) lista(nmax) = {my(list = List(), ndmax = 0, d, s); for(n = 1, nmax, nd = sumdiv(n, d, bitand(d, n)==d); if(nd > ndmax, ndmax = nd; listput(list, n))); Vec(list)};
%Y A359082 Cf. A046801, A246600, A359080, A359081, A359083.
%K A359082 nonn,base
%O A359082 1,2
%A A359082 _Amiram Eldar_, Dec 15 2022
%E A359082 a(28)-a(29) from _Martin Ehrenstein_, Dec 19 2022