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%I #9 Nov 29 2019 18:23:55
%S 1,3,9,15,45,189,765,48573,196605,3183328701,12884901885
%N Numbers all of whose divisors are binary palindromes (A329419) with a record number of divisors.
%C A number m is in this sequence if it is in A329419, and d(m) > d(k) for all terms k < m in A329419, where d(m) is the number of divisors of m (A000005).
%C The corresponding record numbers of divisors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, ...
%C Apparently, the record values are the only values of the number of divisors of the terms of A329419 (checked for all the terms of A329419 below a(11)).
%t binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2];
%t binAllDivPalQ[n_] := binPalQ[n] && AllTrue[Most @ Divisors[n], binPalQ];
%t divNumMax = 0; seq={}; Do[If[binAllDivPalQ[n] && (divNum = DivisorSigma[0, n]) > divNumMax, divNumMax = divNum; AppendTo[seq, n]],{n, 1, 2*10^5}]; seq
%Y Subsequence of A006995 and A329419.
%Y Cf. A000005.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Nov 29 2019
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