Number of the day: 3733

Bartel Leendert van der Waerden was born on this day 115 years ago.

Properties of the number 3733:

3733 is a cyclic number.
3733 is the 521^th prime.
3733 has 9 antidivisors and 3732 totatives.
3733 has sum of divisors equal to 3734 which is semiprime.
Reversing the decimal digits of 3733 results in an emirp.
3733 = 1867² - 1866² is the difference of 2 nonnegative squares in 1 way.
3733 is the sum of 2 positive triangular numbers.
3733 is the difference of 2 positive pentagonal numbers in 1 way.
3733 = 22² + 57² is the sum of 2 positive squares in 1 way.
3733 = 23² + 30² + 48² is the sum of 3 positive squares.
3733² = 2508² + 2765² is the sum of 2 positive squares in 1 way.
3733² is the sum of 3 positive squares.
3733 is a proper divisor of 3³¹¹ - 1.
3733 = '3' + '733' is the concatenation of 2 prime numbers.
3733 is an emirp in (at least) the following bases: 2, 5, 8, 10, 14, 15, 18, 19, 21, 27, 29, 32, 37, 43, 45, 50, 55, 56, 59, 65, 67, 70, 71, 76, 77, 78, 79, 81, 82, 85, 89, 90, 91, 93, 94, 95, 97, and 99.
3733 is palindromic in (at least) the following bases: 23, 41, and -33.
3733 consists of only the digits '3' and '7'.
3733 in base 22 = 7ff and consists of only the digits '7' and 'f'.
3733 in base 23 = 717 and consists of only the digits '1' and '7'.
3733 in base 30 = 44d and consists of only the digits '4' and 'd'.
3733 in base 40 = 2DD and consists of only the digits '2' and 'D'.
3733 in base 41 = 292 and consists of only the digits '2' and '9'.

The number 3733 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006562: Balanced primes (of order one): primes which are the average of the previous prime and the following prime.
A019546: Primes whose digits are primes.
A024770: Right-truncatable primes: every prefix is prime.
A053445: Second differences of partition numbers A000041.
A069489: Primes > 1000 in which every substring of length 3 is also prime.
A081633: Class 5+ primes (for definition see A005105).
A133960: Home primes whose homeliness is 3.
A142199: Primes congruent to 2 mod 41.
A211685: Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).
A226929: Values of n such that L(9) and N(9) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.