Wednesday, June 8, 2016

Number of the day: 9073

Properties of the number 9073:

9073 = 43 × 211 is semiprime and squarefree.
9073 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 8820 totatives.
9073 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 9073 results in a prime.
9073 = 45372 - 45362 = 1272 - 842 is the difference of 2 nonnegative squares in 2 ways.
9073 is the sum of 2 positive triangular numbers.
9073 is the difference of 2 positive pentagonal numbers in 2 ways.
9073 = 92 + 442 + 842 is the sum of 3 positive squares.
90732 is the sum of 3 positive squares.
9073 is a divisor of 8596 - 1.
9073 = '907' + '3' is the concatenation of 2 prime numbers.
9073 is an emirpimes in (at least) the following bases: 6, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 26, 28, 33, 35, 39, 41, 42, 43, 46, 48, 49, 55, 56, 57, 59, 61, 63, 64, 67, 69, 73, 77, 78, 79, 80, 85, 86, 88, 90, 92, 93, 94, 96, and 97.
9073 is palindromic in (at least) the following bases: 72, 81, 84, and -35.
9073 in base 3 = 110110001 and consists of only the digits '0' and '1'.
9073 in base 6 = 110001 and consists of only the digits '0' and '1'.
9073 in base 27 = cc1 and consists of only the digits '1' and 'c'.

The number 9073 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020142: Pseudoprimes to base 14.
A020159: Pseudoprimes to base 31.
A064910: Smallest semiprime p1*p2 such that p2 mod p1 = n.
A069190: Centered 24-gonal numbers.
A074341: a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A078293: Least nontrivial multiple of the n-th prime beginning with 9.
A113690: Semiprimes in A054552.
A118589: E.g.f.: A(x) = exp(x + x^2 + x^3).
A199744: G.f.: 1/(1+x+2*x^2+2*x^3+x^4).
A261764: Triangle read by rows: T(n,k) is the number of nilpotent subpermutations on an n-set, each of nilpotency index less than or equal to k.

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