137968029000 has 320 divisors, whose sum is σ = 488902368240. Its totient is φ = 36285926400.

The previous prime is 137968028993. The next prime is 137968029019. The reversal of 137968029000 is 920869731.

It can be written as a sum of positive squares in 8 ways, for example, as 915546564 + 137052482436 = 30258^2 + 370206^2 .

It is a super-2 number, since 2×137968029000² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 5901334 + ... + 5924666.

Almost surely, 2^137968029000 is an apocalyptic number.

137968029000 is a gapful number since it is divisible by the number (10) 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 137968029000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (244451184120).

137968029000 is an abundant number, since it is smaller than the sum of its proper divisors (350934339240).

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

137968029000 is a wasteful number, since it uses less digits than its factorization.

137968029000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23439 (or 23416 counting only the distinct ones).

The product of its (nonzero) digits is 163296, while the sum is 45.

The spelling of 137968029000 in words is "one hundred thirty-seven billion, nine hundred sixty-eight million, twenty-nine thousand".