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

1,2

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 <...<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

Table of n, a(n) for n=1..63.

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

Cf. A087999, A178864.

Subsequences: A002113, A002385, A062687, A084092.

Sequence in context: A246450 A049814 A028828 * A178864 A058226 A172974

Adjacent sequences: A334136 A334137 A334138 * A334140 A334141 A334142

Keyword

nonn,base

Author

Bernard Schott, Apr 15 2020

Status

approved