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A329420
Numbers all of whose divisors are binary palindromes (A329419) with a record number of divisors.
2
1, 3, 9, 15, 45, 189, 765, 48573, 196605, 3183328701, 12884901885
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)).
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Nov 29 2019
STATUS
approved