Number of the day: 15625

Augustin-Louis Cauchy was born on this day 231 years ago.

Properties of the number 15625:

15625 = 5⁶ is a prime power and not squarefree.
15625 has 1 distinct prime factor, 7 divisors, 12 antidivisors and 12500 totatives.
15625 has a prime digit sum 19 in base 10.
15625 has a triangular digit product 300 in base 10.
15625 has sum of divisors equal to 19531 which is an emirp.
Reversing the decimal digits of 15625 results in a semiprime.
15625 = 125² is a perfect square.
15625 = 4³ + 17³ + 22³ is the sum of 3 positive cubes in 1 way.
15625 = (124 × 125)/2 + (125 × 126)/2 is the sum of at least 2 consecutive triangular numbers in 1 way. In fact, it is the sum of 2 triangular numbers.
15625 = 7813² - 7812² = 1565² - 1560² = 325² - 300² = 125² - 0² is the difference of 2 nonnegative squares in 4 ways.
15625 is the difference of 2 positive pentagonal numbers in 3 ways.
15625 = 75² + 100² = 35² + 120² = 44² + 117² is the sum of 2 positive squares in 3 ways.
15625 is the sum of 3 positive squares.
15625² = 9375² + 12500² = 4375² + 15000² = 5500² + 14625² = 8400² + 13175² = 1185² + 15580² = 10296² + 11753² is the sum of 2 positive squares in 6 ways.
15625² is the sum of 3 positive squares.
15625 is a proper divisor of 1249⁵⁰ - 1.
15625 is palindromic in (at least) the following bases: 24, 37, 55, 93, and -73.
15625 in base 5 = 1000000 and consists of only the digits '0' and '1'.
15625 in base 24 = 1331 and consists of only the digits '1' and '3'.
15625 in base 25 = 1000 and consists of only the digits '0' and '1'.
15625 in base 37 = BFB and consists of only the digits 'B' and 'F'.
15625 in base 39 = AAP and consists of only the digits 'A' and 'P'.
15625 in base 54 = 5JJ and consists of only the digits '5' and 'J'.
15625 in base 55 = 595 and consists of only the digits '5' and '9'.
15625 in base 62 = 441 and consists of only the digits '1' and '4'.

The number 15625 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000351: Powers of 5: a(n) = 5^n.
A000578: The cubes: a(n) = n^3.
A001014: Sixth powers: a(n) = n^6.
A003593: Numbers of the form 3^i*5^j with i, j >= 0.
A007778: a(n) = n^(n+1).
A023194: Numbers n such that sigma(n) (sum of divisors of n) is prime.
A030516: Numbers with 7 divisors. 6th powers of primes.
A133500: The powertrain or power train map: Powertrain(n): if abcd... is the decimal expansion of a number n, then the powertrain of n is the number n' = a^b*c^d* ..., which ends in an exponent or a base according as the number of digits is even or odd. a(0) = 0 by convention.
A191702: Dispersion of A008587 (5,10,15,20,25,30,...), by antidiagonals.
A241909: Self-inverse permutation of natural numbers: a(1)=1, a(p_i) = 2^i, and if n = p_i1 * p_i2 * p_i3 * ... * p_{ik-1} * p_ik, where p's are primes, with their indexes are sorted into nondescending order: i1 <= i2 <= i3 <= ... <= i_{k-1} <= ik, then a(n) = 2^(i1-1) * 3^(i2-i1) * 5^(i3-i2) * ... * p_k^(1+(ik-i_{k-1})). Here k = A001222(n) and ik = A061395(n).