MathDB

a) Does there exist an infinite subset

S

of the natural numbers, such that

S\neq \mathbb{N}

, and such that for each natural number

n\not \in S

, exactly

n

members of

S

are coprime with

n

?
b) Does there exist an infinite subset

S

of the natural numbers, such that for each natural number

n\in S

, exactly

n

members of

S

are coprime with

n

?
Proposed by Morteza Saghafian

Problem Statement