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A330815
Numbers with a record number of divisors whose binary expansion is palindromic.
3
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, ...
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 01 2020
STATUS
approved