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Numbers all of whose divisors are palindromic.
25

%I #34 Nov 24 2019 06:45:32

%S 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,121,131,151,181,191,

%T 202,242,262,303,313,353,363,373,383,393,404,484,505,606,626,707,727,

%U 757,787,797,808,909,919,929,939,1111,1331,1441,1661,1991,2222,2662

%N Numbers all of whose divisors are palindromic.

%H Amiram Eldar, <a href="/A062687/b062687.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..221 from Indranil Ghosh)

%e The divisors of 44 are 1, 2, 4, 11, 22 and 44, which are all palindromes, so 44 is in the sequence.

%e 808 has divisors are 1, 2, 4, 8, 101, 202, 404, 808, so 808 is in the sequence.

%e 818 is palindromic, but since it's 2 * 409, it's not in the sequence.

%p isA062687 := proc(n)

%p for d in numtheory[divisors](n) do

%p if not isA002113(d) then

%p return false;

%p end if;

%p end do;

%p true ;

%p end proc: # _R. J. Mathar_, Sep 09 2015

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

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

%Y Cf. A087991, A084325, A002385 (subset).

%Y Subsequence of A002113.

%K base,easy,nonn

%O 1,2

%A _Erich Friedman_, Jul 04 2001