Number of the day: 6065

Properties of the number 6065:

6065 is a cyclic number.
6065 = 5 × 1213 is semiprime and squarefree.
6065 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 4848 totatives.
6065 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 6065 results in an emirpimes.
6065 = 3033² - 3032² = 609² - 604² is the difference of 2 nonnegative squares in 2 ways.
6065 is the difference of 2 positive pentagonal numbers in 2 ways.
6065 = 32² + 71² = 17² + 76² is the sum of 2 positive squares in 2 ways.
6065 = 16² + 25² + 72² is the sum of 3 positive squares.
6065² = 3639² + 4852² = 2584² + 5487² = 4017² + 4544² = 1225² + 5940² is the sum of 2 positive squares in 4 ways.
6065² is the sum of 3 positive squares.
6065 is a proper divisor of 1931⁴ - 1.
6065 is an emirpimes in (at least) the following bases: 2, 4, 10, 11, 12, 13, 15, 17, 19, 23, 25, 29, 33, 34, 37, 38, 41, 45, 49, 58, 61, 63, 65, 74, 77, 91, 95, and 98.
6065 is palindromic in (at least) base 47.
6065 in base 27 = 88h and consists of only the digits '8' and 'h'.
6065 in base 46 = 2dd and consists of only the digits '2' and 'd'.
6065 in base 47 = 2Z2 and consists of only the digits '2' and 'Z'.

The number 6065 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031127: Number of proper factorizations of p1^n*p2^4, where p1 and p2 are distinct primes.
A046874: Row/column pre-periods of Sprague-Grundy values of Wythoff's Game.
A061294: a(n) = floor( n^Pi ).
A080298: Positions of A080299 in A014486.
A095383: Number of different initial values for 3x+1 trajectories started with initial values not exceeding 2^n and in which the peak values are larger than 2^n.
A116702: Number of permutations of length n which avoid the patterns 123, 3241.
A192706: Number of 6X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 6 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)
A248987: T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having two times the sum of some three elements equal to three times the sum of the remaining two
A294548: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A296275: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1)*b(n), where a(0) = 2, a(1) = 3, b(0) = 1, b(1) = 4, b(2) = 5, and (a(n)) and (b(n)) are increasing complementary sequences.