

A334139


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


3



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, 44, 45, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 101, 105, 110, 111, 120, 121, 126, 131, 132, 140, 141, 151, 154, 161, 165, 168, 171, 180, 181, 191, 198, 202, 210
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OFFSET

1,2


COMMENTS

These terms are the fixed points of A087999.
All the palindromes are in the sequence.
Now, if m is nonpalindromic, 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).
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.


LINKS



EXAMPLE

2, 5, 131 are terms as palindromic primes.
111 = 3 * 37 is a term because 111 is a palindrome, so LCM(1,3,37,111) = 111.
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.


MATHEMATICA

Select[Range[200], LCM @@ Select[Divisors[#], PalindromeQ] == # &] (* Amiram Eldar, Apr 15 2020 *)


PROG

(PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d);
isok(n) = lcm(select(ispal, divisors(n))) == n; \\ Michel Marcus, Apr 16 2020


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



