A192219 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.

1226221, 13488431, 123848321, 12467976421, 1030507050301, 1120237320211, 1225559555221, 1234469644321, 1334459544331, 11335577553311, 100330272033001, 101222252222101, 103023070320301, 113143969341311, 121363494363121, 134312696213431

Offset: 1

Author

Jaroslav Krizek, Jul 13 2011

Keywords

• nonn
• base

Comments

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

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

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

Examples

			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.
		

Programs

Mathematica

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 *)

Extensions

a(5)-a(16) (including six found by T. D. Noe) from Donovan Johnson, Jul 14 2011