1417104000 has 384 divisors, whose sum is σ = 5487889680. Its totient is φ = 348364800.

The previous prime is 1417103971. The next prime is 1417104047. The reversal of 1417104000 is 4017141.

It can be written as a sum of positive squares in 8 ways, for example, as 2742336 + 1414361664 = 1656^2 + 37608^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1871622 + ... + 1872378.

Almost surely, 2^1417104000 is an apocalyptic number.

1417104000 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 1417104000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2743944840).

1417104000 is an abundant number, since it is smaller than the sum of its proper divisors (4070785680).

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

1417104000 is a wasteful number, since it uses less digits than its factorization.

1417104000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 805 (or 780 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 18.

The square root of 1417104000 is about 37644.4418208054. The cubic root of 1417104000 is about 1123.2262418687.

The spelling of 1417104000 in words is "one billion, four hundred seventeen million, one hundred four thousand".