A331663 -id:A331663 - cp's OEIS frontend

A331662 Odd composite numbers k such that the divisors of the binary reversal of k (A030101) are the binary reversals of the divisors of k.

9, 15, 21, 27, 45, 51, 63, 85, 93, 95, 111, 119, 123, 125, 153, 187, 189, 219, 221, 255, 335, 365, 381, 485, 511, 597, 629, 655, 681, 697, 765, 771, 831, 965, 1011, 1139, 1241, 1285, 1389, 1461, 1533, 1535, 1563, 1649, 1731, 1791, 1799, 1983, 2031, 2043, 2045

Offset: 1

Amiram Eldar, Jan 23 2020

			9 is a term since the binary representations of its divisors, 1, 3 and 9, are palindromic: 1, 11 and 1001, i.e., the binary reversals of themselves.
95 is a term since the binary representations of its divisors, 1, 5, 19 and 95, are 1, 101, 10011 and 1011111, and their binary reversals, 1, 101, 11001, 1111101, or  1, 5, 25 and 125 in decimal representation, are the divisors of 125, which is the binary reversal of 95.

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

Cf. A030101.

A329419, A331663 and A331664 are subsequences.

Select[Range[1, 2000, 2], CompositeQ[#] && (Divisors @ IntegerReverse[#, 2]) == IntegerReverse[Divisors[#], 2] &]

A331664 Odd composite numbers k all of whose divisors larger than 1 are not binary palindromes (A006995) such that the divisors of the binary reversal of k (A030101) are the binary reversals of the divisors of k.

Original entry on oeis.org

4847, 5371, 7141, 7913, 22891, 23243, 27053, 27469, 47863, 48599, 60349, 61277, 69211, 73343, 77251, 80623, 81863, 89339, 100201, 111841, 114293, 116729, 126649, 130289, 138623, 180163, 200693, 260833, 286141, 319381, 348121, 371899, 383339, 388561, 439517, 453037

Offset: 1

Amiram Eldar, Jan 23 2020

			4847 is a term since the binary representations of its divisors, 1, 37, 131 and 4847, are 1, 100101, 10000011 and 1001011101111, and their binary reversals, 1, 101001, 11000001 and 1111011101001, or 1, 41, 193 and 7913 in decimal representation, are the divisors of 7913, and none of the divisors of 4847 except 1 are binary palindromes.

Amiram Eldar, Table of n, a(n) for n = 1..2000

Cf. A006995, A030101, A329419.

Subsequence of A331662 and A331663.

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; Select[Range[1, 5*10^5, 2], CompositeQ[#] && (Divisors@IntegerReverse[#, 2]) == IntegerReverse[(d = Divisors[#]), 2] && !AnyTrue[Rest[d], binPalQ] &]

cp's OEIS Frontend

A331662 Odd composite numbers k such that the divisors of the binary reversal of k (A030101) are the binary reversals of the divisors of k.

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