MathDB

Let

n

be a positive integer with at least

4

positive divisors. Let

d(n)

be the number of positive divisors of

n

. Find all values of

n

for which there exists a sequence of

d(n) - 1

positive integers

a_1

a_2

\dots

a_{d(n)-1}

that forms an arithmetic sequence and satisfies the following condition: for any integers

i

and

j

with

1 \leq i < j \leq d(n) - 1

, we have

\gcd(a_i , n) \neq \gcd(a_j , n)

Problem Statement