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

1,2

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