1213129217664 has 1152 divisors, whose sum is σ = 4560215783760. Its totient is φ = 306561024000.

The previous prime is 1213129217659. The next prime is 1213129217683. The reversal of 1213129217664 is 4667129213121.

1213129217664 is a `hidden beast` number, since 1 + 2 + 131 + 292 + 176 + 64 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 32012366400 + 1181116851264 = 178920^2 + 1086792^2 .

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

It is a nude number because it is divisible by every one of its digits.

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, 1835293494 + ... + 1835294154.

Almost surely, 2^{1213129217664} is an apocalyptic number.

1213129217664 is a gapful number since it is divisible by the number (14) 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 1213129217664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2280107891880).

1213129217664 is an abundant number, since it is smaller than the sum of its proper divisors (3347086566096).

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

1213129217664 is a wasteful number, since it uses less digits than its factorization.

1213129217664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 810 (or 788 counting only the distinct ones).

The product of its digits is 217728, while the sum is 45.

The spelling of 1213129217664 in words is "one trillion, two hundred thirteen billion, one hundred twenty-nine million, two hundred seventeen thousand, six hundred sixty-four".