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A329100 Composite palindromes whose divisors > 1 are all nontrivial palindromes (i.e., palindromes with at least two digits).

%I A329100 #32 Nov 08 2019 21:08:12
%S A329100 121,1111,1331,1441,1661,1991,3443,3883,7997,10201,12221,13231,14641,
%T A329100 15251,15851,18281,19291,31613,35653,37673,37873,38683,112211,113311,
%U A329100 115511,116611,124421,125521,134431,136631,139931,145541,146641,157751,167761,169961,176671
%N A329100 Composite palindromes whose divisors > 1 are all nontrivial palindromes (i.e., palindromes with at least two digits).
%C A329100 This is the intersection of A062687 and A038511.
%C A329100 From _Chai Wah Wu_, Nov 08 2019 : (Start)
%C A329100 All terms start and end with the digits 1,3,7 or 9.
%C A329100 First term with 3 prime factors: 1331 = 11^3.
%C A329100 First term with 3 distinct prime factors: 145541 = 11*101*131.
%C A329100 First term with 4 prime factors: 14641 = 11^4.
%C A329100 First term with 5 prime factors: 1478741 = 11^4*101.
%C A329100 No term with more than 3 distinct prime factors or more than 5 prime factors among first 10000 terms.
%C A329100 (End)
%H A329100 Chai Wah Wu, <a href="/A329100/b329100.txt">Table of n, a(n) for n = 1..10000</a>
%e A329100 For k = 1331, its divisors > 1 are 11, 121 and 1331, all of which are palindromes with at least two digits, so 1331 is a term.
%e A329100 For k = 167761, its divisors > 1 are 11, 101, 151, 1111, 1661, 15251 and 167761, all of which are palindromes with at least two digits, so 167761 is a term.
%t A329100 aQ[n_] := CompositeQ[n] && AllTrue[Rest @ Divisors[n], # > 10 && PalindromeQ @ IntegerDigits[#] &]; Select[Range[200000], aQ] (* _Amiram Eldar_, Nov 06 2019 *)
%o A329100 (PARI) isA329100(n) = if((n>1) && !isprime(n) && gcd(n,210)==1, {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd); }, 0) \\ _Jianing Song_, Nov 06 2019, based on the program of A062687
%Y A329100 Cf. A008364, A038511, A062687.
%K A329100 nonn,base
%O A329100 1,1
%A A329100 _Maxim Veselov_, Nov 04 2019
%E A329100 More terms from _Jianing Song_, Nov 06 2019