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

1,2

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A087991, A084325, A002385 (subset).

Subsequence of A002113.

Sequence in context: A110785 A193413 A087992 * A109882 A109872 A030285

Adjacent sequences: A062684 A062685 A062686 * A062688 A062689 A062690

Keyword

base,easy,nonn

Author

Erich Friedman, Jul 04 2001

Status

approved