

A329420


Numbers all of whose divisors are binary palindromes (A329419) with a record number of divisors.


1



1, 3, 9, 15, 45, 189, 765, 48573, 196605, 3183328701, 12884901885
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OFFSET

1,2


COMMENTS

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).
The corresponding record numbers of divisors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, ...
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)).


LINKS

Table of n, a(n) for n=1..11.


MATHEMATICA

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2];
binAllDivPalQ[n_] := binPalQ[n] && AllTrue[Most @ Divisors[n], binPalQ];
divNumMax = 0; seq={}; Do[If[binAllDivPalQ[n] && (divNum = DivisorSigma[0, n]) > divNumMax, divNumMax = divNum; AppendTo[seq, n]], {n, 1, 2*10^5}]; seq


CROSSREFS

Subsequence of A006995 and A329419.
Cf. A000005.
Sequence in context: A188597 A330815 A338611 * A120403 A247967 A062804
Adjacent sequences: A329417 A329418 A329419 * A329421 A329422 A329423


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Nov 29 2019


STATUS

approved



