102616416 has 288 divisors, whose sum is σ = 368686080. Its totient is φ = 27184896.

The previous prime is 102616391. The next prime is 102616421. The reversal of 102616416 is 614616201.

102616416 is a `hidden beast` number, since 1 + 0 + 2 + 616 + 41 + 6 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a self number, because there is not a number n which added to its sum of digits gives 102616416.

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, 2183305 + ... + 2183351.

It is an arithmetic number, because the mean of its divisors is an integer number (1280160).

Almost surely, 2^102616416 is an apocalyptic number.

102616416 is a gapful number since it is divisible by the number (16) 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 102616416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184343040).

102616416 is an abundant number, since it is smaller than the sum of its proper divisors (266069664).

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

102616416 is a wasteful number, since it uses less digits than its factorization.

102616416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 111 (or 78 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 102616416 is about 10129.9761105345. The cubic root of 102616416 is about 468.1721917329.

It can be divided in two parts, 1026 and 16416, that multiplied together give a square (16842816 = 4104²).

The spelling of 102616416 in words is "one hundred two million, six hundred sixteen thousand, four hundred sixteen".