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A334139 Numbers that are equal to the LCM of their palindromic divisors.

%I A334139 #40 Aug 31 2021 01:12:46
%S A334139 1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,20,21,22,24,28,30,33,35,36,40,42,
%T A334139 44,45,55,56,60,63,66,70,72,77,84,88,90,99,101,105,110,111,120,121,
%U A334139 126,131,132,140,141,151,154,161,165,168,171,180,181,191,198,202,210
%N A334139 Numbers that are equal to the LCM of their palindromic divisors.
%C A334139 These terms are the fixed points of A087999.
%C A334139 All the palindromes are in the sequence.
%C A334139 Now, if m is non-palindromic, then m is a term iff m = q_1^r_1 *...* q_i^r_i *...* q_k^r_k, where q_1 <...<q_i <...<q_k are primes, k>=2, r_i >= 1 and every divisor q_i^r_i is a palindrome; these q_i^r_i are in A084092 (see examples).
%C A334139 The first 40 terms, from 1 to 99, are exactly the 40 smallest divisors of 27720, hence the first 40 terms of A178864, but this sequence, which is infinite, is not a duplicate. Also, 27720 is in this sequence.
%e A334139 2, 5, 131 are terms as palindromic primes.
%e A334139 111 = 3 * 37 is a term because 111 is a palindrome, so LCM(1,3,37,111) = 111.
%e A334139 27720 = 2^3 * 3^2 * 5 * 7 * 11, every 2^3=8, 3^2=9, 5, 7, 11 is a palindrome so 27720 is another term, no palindromic.
%t A334139 Select[Range[200], LCM @@ Select[Divisors[#], PalindromeQ] == # &] (* _Amiram Eldar_, Apr 15 2020 *)
%o A334139 (PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d);
%o A334139 isok(n) = lcm(select(ispal,  divisors(n))) == n; \\ _Michel Marcus_, Apr 16 2020
%Y A334139 Cf. A087999, A178864.
%Y A334139 Subsequences: A002113, A002385, A062687, A084092.
%K A334139 nonn,base
%O A334139 1,2
%A A334139 _Bernard Schott_, Apr 15 2020