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138624 = 273192
BaseRepresentation
bin100001110110000000
321001011020
4201312000
513413444
62545440
71115103
oct416600
9231136
10138624
1195172
1268280
134b135
143873a
152b119
hex21d80

138624 has 48 divisors (see below), whose sum is σ = 388620. Its totient is φ = 43776.

The previous prime is 138617. The next prime is 138629. The reversal of 138624 is 426831.

Multipling 138624 by its sum of digits (24), we get a square (3326976 = 18242).

138624 divided by its sum of digits (24) gives a square (5776 = 762).

138624 = T115 + T116 + ... + T132.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×1386242 = 38433226752, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

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

It is one of the 548 Lynch-Bell numbers.

Its product of digits (1152) is a multiple of the sum of its prime divisors (24).

It is a junction number, because it is equal to n+sod(n) for n = 138594 and 138603.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138629) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 7287 + ... + 7305.

138624 is a Friedman number, since it can be written as 6*(38*4)^(2*1), using all its digits and the basic arithmetic operations.

2138624 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (194310).

138624 is an abundant number, since it is smaller than the sum of its proper divisors (249996).

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

138624 is an equidigital number, since it uses as much as digits as its factorization.

138624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 55 (or 24 counting only the distinct ones).

The product of its digits is 1152, while the sum is 24.

The square root of 138624 is about 372.3224409030. The cubic root of 138624 is about 51.7542646256.

The spelling of 138624 in words is "one hundred thirty-eight thousand, six hundred twenty-four".

Divisors: 1 2 3 4 6 8 12 16 19 24 32 38 48 57 64 76 96 114 128 152 192 228 304 361 384 456 608 722 912 1083 1216 1444 1824 2166 2432 2888 3648 4332 5776 7296 8664 11552 17328 23104 34656 46208 69312 138624