A329420 Numbers all of whose divisors are binary palindromes (A329419) with a record number of divisors.

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

Offset: 1

Author

Amiram Eldar, Nov 29 2019

Keywords

• nonn
• more

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)).

Crossrefs

Subsequence of A006995 and A329419.

Cf. A000005.

Programs

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