1006417920 has 144 divisors (see below), whose sum is σ = 3237638040. Its totient is φ = 266895360.

The previous prime is 1006417913. The next prime is 1006417933. The reversal of 1006417920 is 297146001.

1006417920 = T₁₁ + T₁₂ + ... + T₁₈₂₀.

It is a happy number.

1006417920 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5560230 + ... + 5560410.

Almost surely, 2^1006417920 is an apocalyptic number.

1006417920 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1006417920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1618819020).

1006417920 is an abundant number, since it is smaller than the sum of its proper divisors (2231220120).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

1006417920 is an frugal number, since it uses more digits than its factorization.

1006417920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 392 (or 191 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 30.

The square root of 1006417920 is about 31724.0905306992. The cubic root of 1006417920 is about 1002.1347462822.

Multiplying 1006417920 by its sum of digits (30), we get a square (30192537600 = 173760²).

1006417920 divided by its sum of digits (30) gives a square (33547264 = 5792²).

The spelling of 1006417920 in words is "one billion, six million, four hundred seventeen thousand, nine hundred twenty".