4

4

Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).

Reads the same in both directions.

Divisible by 2.

Composite — it factors as 2^2.

1 distinct prime factor, 2 with multiplicity.

At least one prime appears squared.

A product of exactly two primes, counted with multiplicity.

A single prime raised to a power.

Every prime factor appears at least squared.

Zero, because a squared prime divides n.

A gap of 2 between them.

1, 2, 4

The proper divisors — everything except n itself.

Its proper divisors fall short by 1.

How many integers from 1 to n share no factor with n.

0² + 2² = 4

Legendre's three-square theorem allows it.

Lagrange's four-square theorem: every non-negative integer is, without exception.

The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.

Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.

Every single-digit number equals itself raised to the first power, so all ten qualify trivially.

Divisible by its digit sum 4 — 4 ÷ 4 = 1.

Peaks at 4 along the way.