[PDF][PDF] Palindromic Sums of Proper Divisors.

P Pollack - Integers, 2015 - pollack.uga.edu
P Pollack
Integers, 2015pollack.uga.edu
Fix an integer g≥ 2. A natural number n is called a palindrome in base g if its base g
expansion reads the same forwards and backwards. Let s (n)=∑ d| n, d< nd be the sum-of-
proper-divisors function. We show that for almost all (that is, asymptotically 100% of) natural
numbers n, s (n) is not a palindrome in base g. We also show how to reach the same
conclusion for several other commonly occurring arithmetic functions.
Abstract
Fix an integer g≥ 2. A natural number n is called a palindrome in base g if its base g expansion reads the same forwards and backwards. Let s (n)=∑ d| n, d< n d be the sum-of-proper-divisors function. We show that for almost all (that is, asymptotically 100% of) natural numbers n, s (n) is not a palindrome in base g. We also show how to reach the same conclusion for several other commonly occurring arithmetic functions.
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