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 A359083 #6 Dec 17 2022 08:26:40
%S A359083 1,3,15,63,255,891,4095,262143,1048575,16777215,68719476735
%N A359083 Numbers k such that A246600(k) = A000005(k) and A000005(k) sets a new record.
%C A359083 Numbers k with a record number of divisors, such that for all the divisors d of k 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 A359083 All the terms are odd since all the terms of A359080 are odd.
%C A359083 The corresponding numbers of divisors are 1, 2, 4, 6, 8, 10, 24, 32, 48, 96, 512, ... .
%C A359083 a(12) > 3*10^11, if it exists.
%H A359083 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A359083 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.
%t A359083 s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; seq={}; dm = 0; Do[d = DivisorSigma[0, n]; If[d > dm && d == s[n], dm = d; AppendTo[seq, n]], {n, 1, 2*10^7}]; seq
%o A359083 (PARI) lista(nmax) = {my(list = List(), ndmax = 0, d, s); for(n = 1, nmax, nd = numdiv(n); if(nd > ndmax && sumdiv(n, d, bitand(d, n)==d) == nd, ndmax = nd; listput(list, n))); Vec(list)};
%Y A359083 Subsequence of A359080.
%Y A359083 Cf. A000005, A246600, A359081, A359082.
%K A359083 nonn,base,more
%O A359083 1,2
%A A359083 _Amiram Eldar_, Dec 15 2022