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

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

Offset: 1

Author

Bernard Schott, Apr 15 2020

Keywords

• nonn
• base

Comments

These terms are the fixed points of A087999.

All the palindromes are in the sequence.

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 <...=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.

Examples

			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.
		

Crossrefs

Cf. A087999, A178864.

Subsequences: A002113, A002385, A062687, A084092.

Programs

Mathematica

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

PARI

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