A330815 Numbers with a record number of divisors whose binary expansion is palindromic.

1, 3, 9, 15, 45, 135, 189, 315, 495, 765, 2079, 3465, 4095, 8415, 12285, 45045, 69615, 135135, 405405, 528255, 675675, 765765, 2297295, 5810805, 11486475, 17432415, 29054025, 32927895, 43648605, 50331645, 98783685, 184549365, 296351055, 392837445, 553648095

Offset

1,2

Comments

Indices of records of A175242.

The corresponding number of binary palindromic divisors are 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 15, 17, 18, 22, 26, 27, 33, 34, 35, 37, 39, 47, 50, 51, 54, 55, 56, 57, 60, 70, 71, 74, 76, 90, ...

Links

Table of n, a(n) for n=1..35.

Example

9 is a term since it has 3 binary palindromic divisors, 1, 3 and 9, whose binary representations are 1, 11 and 1001. All the numbers below 9 have less than 3 binary palindromic divisors.

Mathematica

binPalDiv[n_] := DivisorSum[n, 1 &, PalindromeQ @ IntegerDigits[#, 2] &];  bmax = 0; seq = {}; Do[b = binPalDiv[n]; If[b > bmax, bmax = b; AppendTo[seq, n]], {n, 1, 10^5}]; seq

Crossrefs

Cf. A006995, A175242, A329419.

Sequence in context: A140864 A171929 A188597 * A338611 A329420 A120403

Adjacent sequences: A330812 A330813 A330814 * A330816 A330817 A330818

Keyword

nonn,base

Author

Amiram Eldar, Jan 01 2020

Status

approved