MathDB

A set of positive integers is said to be pilak if it can be partitioned into 2 disjoint subsets

F

and

T

, each with at least

2

elements, such that the elements of

F

are consecutive Fibonacci numbers, and the elements of

T

are consecutive triangular numbers. Find all positive integers

n

such that the set containing all the positive divisors of

n

except

n

itself is pilak.

Problem Statement