A331664 - OEIS

%I #10 Jan 25 2020 09:08:02

%S 4847,5371,7141,7913,22891,23243,27053,27469,47863,48599,60349,61277,

%T 69211,73343,77251,80623,81863,89339,100201,111841,114293,116729,

%U 126649,130289,138623,180163,200693,260833,286141,319381,348121,371899,383339,388561,439517,453037

%N 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.

%H Amiram Eldar, <a href="/A331664/b331664.txt">Table of n, a(n) for n = 1..2000</a>

%e 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.

%t 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] &]

%Y Cf. A006995, A030101, A329419.

%Y Subsequence of A331662 and A331663.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Jan 23 2020