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Numbers m such that set of divisors of m is equal to set of reversals of divisors of m but all divisors of m are not palindromic.
0

%I #20 Aug 03 2014 14:01:31

%S 1226221,13488431,123848321,12467976421,1030507050301,1120237320211,

%T 1225559555221,1234469644321,1334459544331,11335577553311,

%U 100330272033001,101222252222101,103023070320301,113143969341311,121363494363121,134312696213431

%N Numbers m such that set of divisors of m is equal to set of reversals of divisors of m but all divisors of m are not palindromic.

%C All terms are palindromic (subsequence of A002113 - palindromic numbers).

%C Subsequence of A188650 (numbers that are divisible by all reversals of their divisors).

%C Union a(n) and A062687 (numbers all of whose divisors are palindromic) is sequence of numbers m such that set of divisors of m is equal to set of reversals of divisors of m: {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 121, 131, ..., 1226221, ...). - Jaroslav Krizek, Jul 18 2011.

%e 1226221 has divisors 1, 1021, 1201, 1226221. Set of divisors is equal to set of reversals of divisors. Divisors 1021 and 1201 are not palindromic.

%t t = Union[Flatten[Table[d = IntegerDigits[n]; {FromDigits[Join[d, Reverse[d]]], FromDigits[Join[d, Reverse[Most[d]]]]}, {n, 0, 99999}]]]; okQ[n_] := Module[{f = Divisors[n], r}, r = f; Do[r[[i]] = FromDigits[Reverse[IntegerDigits[f[[i]]]]], {i, Length[f]}]; f == Sort[r] && f != r]; Select[t, okQ] (* _T. D. Noe_, Jul 14 2011 *)

%K nonn,base

%O 1,1

%A _Jaroslav Krizek_, Jul 13 2011

%E a(5)-a(16) (including six found by T. D. Noe) from _Donovan Johnson_, Jul 14 2011