

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.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

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


EXAMPLE

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.


MATHEMATICA

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] &]


CROSSREFS

Cf. A006995, A030101, A329419.
Subsequence of A331662 and A331663.
Sequence in context: A185990 A215949 A031838 * A031826 A243835 A124088
Adjacent sequences: A331661 A331662 A331663 * A331665 A331666 A331667


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Jan 23 2020


STATUS

approved



