A062687 Numbers all of whose divisors are palindromic.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 121, 131, 151, 181, 191, 202, 242, 262, 303, 313, 353, 363, 373, 383, 393, 404, 484, 505, 606, 626, 707, 727, 757, 787, 797, 808, 909, 919, 929, 939, 1111, 1331, 1441, 1661, 1991, 2222, 2662

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			The divisors of 44 are 1, 2, 4, 11, 22 and 44, which are all palindromes, so 44 is in the sequence.
808 has divisors are 1, 2, 4, 8, 101, 202, 404, 808, so 808 is in the sequence.
818 is palindromic, but since it's 2 * 409, it's not in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..221 from Indranil Ghosh)

Crossrefs

Cf. A087991, A084325, A002385 (subset).

Subsequence of A002113.

Programs

Maple

isA062687 := proc(n)
    for d in numtheory[divisors](n) do
        if not isA002113(d) then
            return false;
        end if;
    end do;
    true ;
end proc: # R. J. Mathar, Sep 09 2015

Mathematica

palQ[n_] := Module[{idn = IntegerDigits[n]}, idn == Reverse[idn]]; Select[Range[2750], And@@palQ/@Divisors[#] &] (* Harvey P. Dale, Feb 27 2012 *)

PARI

isok(n) = {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd);} \\ Michel Marcus, Oct 10 2014