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A261534 Nonprime palindromes n with only the digits 0, 1, 2 such that the product of divisors of n is also a palindrome.

%I A261534 #19 Feb 03 2020 10:56:33
%S A261534 1,22,111,121,202,1001,1111,10001,10201,11111,100001,1000001,1001001,
%T A261534 1012101,1100011,1101011,1111111,10000001,100000001,101000101,
%U A261534 110000011,200010002,10000000001,10011111001,11000100011,11001010011,11100100111,11101010111,20000100002
%N A261534 Nonprime palindromes n with only the digits 0, 1, 2 such that the product of divisors of n is also a palindrome.
%C A261534 A subsequence of A244423.
%H A261534 Chai Wah Wu, <a href="/A261534/b261534.txt">Table of n, a(n) for n = 1..203</a>
%t A261534 lim = 1000000; palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; c = Complement[Range@ lim, Prime@ Range@ PrimePi@ lim]; t = Select[c, Total@ Take[RotateRight@ DigitCount@ #, -7] == 0 &]; Select[t, palQ[Times @@ Divisors@ #] &] (* _Michael De Vlieger_, Sep 02 2015 *)
%t A261534 Rest[Select[FromDigits/@Tuples[{0,1,2},11],!PrimeQ[#]&&AllTrue[{#,Times@@ Divisors[ #]},PalindromeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 02 2020 *)
%o A261534 (Python)
%o A261534 from __future__ import division
%o A261534 from sympy import divisor_count
%o A261534 from gmpy2 import isqrt, t_divmod, digits
%o A261534 def palgen(l,b=10): # generator of palindromes in base b of length <= 2*l
%o A261534     if l > 0:
%o A261534         yield 0
%o A261534         for x in range(1,l+1):
%o A261534             n = b**(x-1)
%o A261534             n2 = n*b
%o A261534             for y in range(n,n2):
%o A261534                 k, m = y//b, 0
%o A261534                 while k >= b:
%o A261534                     k, r = t_divmod(k,b)
%o A261534                     m = b*m + r
%o A261534                 yield y*n + b*m + k
%o A261534             for y in range(n,n2):
%o A261534                 k, m = y, 0
%o A261534                 while k >= b:
%o A261534                     k, r = t_divmod(k,b)
%o A261534                     m = b*m + r
%o A261534                 yield y*n2 + b*m + k
%o A261534 A261534_list = [1]
%o A261534 for m in palgen(17,3):
%o A261534     n = int(digits(m,3))
%o A261534     d = int(divisor_count(n))
%o A261534     if d > 2:
%o A261534         q, r = t_divmod(d,2)
%o A261534         s = digits(n**q*(isqrt(n) if r else 1))
%o A261534         if s == s[::-1]:
%o A261534             A261534_list.append(n)
%Y A261534 Cf. A244411, A244423.
%K A261534 nonn,base
%O A261534 1,2
%A A261534 _Chai Wah Wu_, Aug 31 2015