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
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)
Programs
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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
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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