416152509953664 has 512 divisors, whose sum is σ = 1230718095360000. Its totient is φ = 123527052247040.

The previous prime is 416152509953651. The next prime is 416152509953699. The reversal of 416152509953664 is 466359905251614.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (66).

It is a junction number, because it is equal to n+sod(n) for n = 416152509953595 and 416152509953604.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 186031518754 + ... + 186031520990.

It is an arithmetic number, because the mean of its divisors is an integer number (2403746280000).

Almost surely, 2^{416152509953664} is an apocalyptic number.

416152509953664 is a gapful number since it is divisible by the number (44) 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 416152509953664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (615359047680000).

416152509953664 is an abundant number, since it is smaller than the sum of its proper divisors (814565585406336).

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

416152509953664 is a wasteful number, since it uses less digits than its factorization.

416152509953664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4656 (or 4644 counting only the distinct ones).

The product of its (nonzero) digits is 209952000, while the sum is 66.

The spelling of 416152509953664 in words is "four hundred sixteen trillion, one hundred fifty-two billion, five hundred nine million, nine hundred fifty-three thousand, six hundred sixty-four".