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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 (list; graph; refs; listen; history; text; internal format)
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 40 first terms of A178864, but this sequence that 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

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Last modified June 13 09:02 EDT 2021. Contains 344981 sequences. (Running on oeis4.)