513191408897664 has 1152 divisors, whose sum is σ = 1864161510382080. Its totient is φ = 139951517368320.

The previous prime is 513191408897659. The next prime is 513191408897677. The reversal of 513191408897664 is 466798804191315.

513191408897664 is a `hidden beast` number, since 5 + 1 + 3 + 1 + 91 + 408 + 8 + 9 + 76 + 64 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a junction number, because it is equal to n+sod(n) for n = 513191408897592 and 513191408897601.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 3448954852 + ... + 3449103644.

It is an arithmetic number, because the mean of its divisors is an integer number (1618195755540).

Almost surely, 2^{513191408897664} is an apocalyptic number.

513191408897664 is a gapful number since it is divisible by the number (54) 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 513191408897664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (932080755191040).

513191408897664 is an abundant number, since it is smaller than the sum of its proper divisors (1350970101484416).

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

513191408897664 is a wasteful number, since it uses less digits than its factorization.

513191408897664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 148940 (or 148909 counting only the distinct ones).

The product of its (nonzero) digits is 313528320, while the sum is 72.

The spelling of 513191408897664 in words is "five hundred thirteen trillion, one hundred ninety-one billion, four hundred eight million, eight hundred ninety-seven thousand, six hundred sixty-four".