414138146240 has 896 divisors, whose sum is σ = 1315078668288. Its totient is φ = 120720015360.

The previous prime is 414138146239. The next prime is 414138146251. The reversal of 414138146240 is 42641831414.

It is a super-2 number, since 2×414138146240² (a number of 24 digits) contains 22 as substring.

It is a junction number, because it is equal to n+sod(n) for n = 414138146194 and 414138146203.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 1824397007 + ... + 1824397233.

It is an arithmetic number, because the mean of its divisors is an integer number (1467721728).

Almost surely, 2^414138146240 is an apocalyptic number.

414138146240 is a gapful number since it is divisible by the number (40) 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 414138146240, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (657539334144).

414138146240 is an abundant number, since it is smaller than the sum of its proper divisors (900940522048).

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

414138146240 is a wasteful number, since it uses less digits than its factorization.

414138146240 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 385 (or 375 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 38.

Adding to 414138146240 its reverse (42641831414), we get a palindrome (456779977654).

The spelling of 414138146240 in words is "four hundred fourteen billion, one hundred thirty-eight million, one hundred forty-six thousand, two hundred forty".