416101065216000 has 1664 divisors, whose sum is σ = 1564500710822400. Its totient is φ = 97572932812800.

The previous prime is 416101065215911. The next prime is 416101065216007. The reversal of 416101065216000 is 612560101614.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416101065216007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 36217338256 + ... + 36217349744.

It is an arithmetic number, because the mean of its divisors is an integer number (940204754100).

Almost surely, 2^{416101065216000} is an apocalyptic number.

416101065216000 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 416101065216000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (782250355411200).

416101065216000 is an abundant number, since it is smaller than the sum of its proper divisors (1148399645606400).

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

416101065216000 is a wasteful number, since it uses less digits than its factorization.

416101065216000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11640 (or 11608 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 33.

It can be divided in two parts, 41610 and 1065216000, that multiplied together give a square (44323637760000 = 6657600²).

The spelling of 416101065216000 in words is "four hundred sixteen trillion, one hundred one billion, sixty-five million, two hundred sixteen thousand".