A329419 Numbers all of whose divisors are binary palindromes.

1, 3, 5, 7, 9, 15, 17, 21, 27, 31, 45, 51, 63, 73, 85, 93, 107, 119, 127, 153, 189, 219, 255, 257, 313, 365, 381, 443, 511, 765, 771, 1193, 1241, 1285, 1453, 1533, 1571, 1619, 1787, 1799, 1831, 1879, 2313, 3579, 3855, 4369, 4889, 5113, 5189, 5397, 5557, 5869

Offset: 1

Author

Amiram Eldar, Nov 29 2019

Keywords

• nonn
• base

Comments

Subsequence of A163410, and differs from it from n = 65.

Examples

			15 is in the sequence since the binary representations of its divisors, 1, 3, 5, and 15, are all palindromes: 1, 11, 101, and 1111.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006995, A062687, A163410.

Supersequence of A016041.

Programs

Mathematica

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; seqQ[n_] := binPalQ[n] && AllTrue[Most @ Divisors[n], binPalQ]; Select[Range[10^4], seqQ]