Number of the day: 8167

Pierre Joseph Louis Fatou was born on this day 140 years ago.

Properties of the number 8167:

8167 is a cyclic number.
8167 is the 1025^th prime.
8167 has 23 antidivisors and 8166 totatives.
8167 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 8167 results in a sphenic number.
8167 = 4084² - 4083² is the difference of 2 nonnegative squares in 1 way.
8167 is the difference of 2 positive pentagonal numbers in 1 way.
8167 is not the sum of 3 positive squares.
8167² is the sum of 3 positive squares.
8167 is a proper divisor of 2¹³⁶¹ - 1.
8167 is an emirp in (at least) the following bases: 16, 23, 25, 27, 29, 33, 35, 41, 47, 49, 57, 66, 67, 73, 74, 76, 78, 79, 81, 85, 88, 91, 96, 99, and 100.
8167 is palindromic in (at least) the following bases: 32, 34, 52, -21, and -71.
8167 in base 32 = 7v7 and consists of only the digits '7' and 'v'.
8167 in base 33 = 7gg and consists of only the digits '7' and 'g'.
8167 in base 34 = 727 and consists of only the digits '2' and '7'.
8167 in base 51 = 377 and consists of only the digits '3' and '7'.
8167 in base 52 = 313 and consists of only the digits '1' and '3'.

The number 8167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002846: Number of ways of transforming a set of n indistinguishable objects into n singletons via a sequence of n-1 refinements.
A039726: Recursive prime generating sequence.
A045714: Primes with first digit 8.
A051439: a(n) = prime(2^n+1).
A054564: Prime number spiral (clockwise, Southeast spoke).
A081634: Class 6+ primes.
A158713: Primes p such that p1=Ceiling[p/2]+p is prime and p2=Ceiling[p1/2]+p is prime.
A227515: Values of n such that L(12) and N(12) 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.
A236365: Primes whose binary and octal representation are also prime when read in decimal.
A291631: Numbers k such that 6 is the smallest decimal digit of k^2.