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

Author

Amiram Eldar, Jan 01 2020

Keywords

• nonn
• base

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, ...

Examples

			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.
		

Crossrefs

Cf. A006995, A175242, A329419.

Programs

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