Sun's quadratic practical-values conjecture

Let a,b,ca,b,c be positive integers with 2midab2 mid ab and 2dividesc2 divides c. A practical number is a positive integer each of whose integers from 11 through it can be written as a \sum of distinct divisors. Sun's quadratic practical-values conjecture. There are infinitely many ninn in\natural such that an2+bn+can^2+bn+c is practical. Moreover, when a=1a=1, there is an integer nn satisfying 1<nmax{b,c}1<n\leq\max\{b,c\} such that n2+bn+cn^2+bn+c is practical. The conjecture is motivated by computational evidence, and the source gives no resolution.

Sources & referencesView supporting material

Primary source

Li-Yuan Wang and Zhi-Wei Sun, “On practical numbers of some special forms”, arXiv:1809.01532 (2019).

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