Number Theory

   

Palindromic Abundant Numbers P for Which P-Q^2+1 is an Abundant Number for Any Q Prime Greater Than 3

Authors: Marius Coman

In this paper I make the following observation: there exist palindromic abundant numbers P such that n = P – q^2 + 1 is an abundant number for any q prime, q ≥ 5 (of course, for q^2 < P + 1). The first such P is the first palindromic abundant number 66 (with corresponding [q, n] = [5, 42], [7, 18]. Another such palindromic abundant numbers are 222, 252, 282, 414, 444, 474, 606, 636, 666. Up to 666, the palindromic abundant numbers 88, 272, 464, 616 don’t have this property. Questions: are there infinite many such palindromic abundant numbers? What other sets of integers have this property beside palindromic abundant numbers?

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Submission history

[v1] 2018-01-14 05:43:59

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