A334392 Numbers m such that the LCM of their palindromic divisors is neither 1 nor m.

16, 25, 26, 27, 32, 34, 38, 39, 46, 48, 49, 50, 51, 52, 54, 57, 58, 62, 64, 65, 68, 69, 74, 75, 76, 78, 80, 81, 82, 85, 86, 87, 91, 92, 93, 94, 95, 96, 98, 100, 102, 104, 106, 108, 112, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 128, 129, 130, 133, 134

Offset: 1

Author

Bernard Schott, May 04 2020

Keywords

• nonn
• base

Comments

A334139, A334391 and this sequence form a partition of the set of positive integers N* (A000027).

The integers {2^k, k >= 4, 2^k non-palindrome} form a subsequence whose first few terms are : 16, 32, 64, 128, ...

Examples

			50 has 3 palindromic divisors {1, 2, 5} then A087999(50) = 10 and 50 is a term.
		

Links

• Wikipedia, Partition of a set

Crossrefs

Cf. A087990, A087999.

Cf. A334391 [LCM(palindromic divisors of m) = 1], A334139 [LCM(palindromic divisors of m) = m], this sequence [LCM(palindromic divisors of m) != 1 and != m].

Programs

Mathematica

Select[Range[125], !MemberQ[{1, #}, LCM @@ Select[Divisors[#], PalindromeQ]] &] (* Amiram Eldar, May 05 2020 *)

PARI

ispal(x) = my(d=digits(x)); d == Vecrev(d);
isok(m) = my(d=divisors(m), lcmpd = lcm(select(x->ispal(x), d))); (lcmpd != 1) && (lcmpd != m); \\ Michel Marcus, May 05 2020