Six of the factors of 1221 are palindromes: {1,3,11,33,111,1221} but two are not: {37,407}
(A) What number under one million has the most palindrome factors?
Some numbers have only palindromes as factors. Examples include 88: {1,2,4,8,11,22,44,88} and any palindromic prime
(B) Find the smallest number with at least as many palindrome factors as part (A) but having only palindrome factors.
When I thought up this problem last month (which had a lot of palindrome dates: 2/2x/22 some of which have a lot of palindrome factors) it was natural to ask for part (A). I realized this wouldn't be too hard to find.
I wanted to ask about numbers with only palindrome factors as well. I ended up going with the current (B) which may be too hard.
If instead of asking for the smallest, I had asked for any number with all palindrome factors and more than part (A) then maybe it won't be so hard.
If 448844 has 18 palindrome factors then multiplying this by palindrome prime of the form 10...010...01 with enough 0's between the 1's will make a new number with twice as many factors. I was unable to find a large enough list of such numbers, though.
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Posted by Jer
on 2022-03-15 10:50:18 |
My thoughts on the difficulty of part (B)
