A261245 The 21 palindromic divisors of the palindrome 12345678987654321.

1, 3, 9, 111, 333, 999, 12321, 36963, 1001001, 3003003, 9009009, 111111111, 333333333, 999999999, 12333333321, 36999999963, 1002003002001, 3006009006003, 111222333222111, 333666999666333, 12345678987654321

Offset: 1

Author

Wolfdieter Lang, Aug 22 2015

Keywords

• nonn
• easy
• base
• fini
• full

Comments

There are 45 divisors of 12345678987654321.

Motivated by A261072 by Ilya Gutkovskiy, which has only six palindromic divisors, namely 1, 3, 7, 9, 171, 1234567890987654321.

12345678987654321 = A002275(9)^2 = 111111111^2 (observed by Jon E. Schoenfield). The repunit R(9) has the eight palindromic divisors 1, 3, 9, 111, 333, 1001001, 3003003, 111111111.

All entries a(n) can be obtained by multiplying two palindromic divisors of R(9).

Crossrefs

Cf. A002275, A261072.

Programs

Mathematica

Select[Divisors[12345678987654321],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2019 *)