Number of the day: 3193

Marius Sophus Lie was born on this day 178 years ago.

Properties of the number 3193:

3193 is a cyclic number.
3193 = 31 × 103 is semiprime and squarefree.
3193 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 3060 totatives.
Reversing the decimal digits of 3193 results in a sphenic number.
3193 = 1597² - 1596² = 67² - 36² is the difference of 2 nonnegative squares in 2 ways.
3193 is the sum of 2 positive triangular numbers.
3193 is the difference of 2 positive pentagonal numbers in 2 ways.
3193 = 9² + 14² + 54² is the sum of 3 positive squares.
3193² is the sum of 3 positive squares.
3193 is a proper divisor of 619² - 1.
3193 = '3' + '193' is the concatenation of 2 prime numbers.
3193 is an emirpimes in (at least) the following bases: 8, 9, 20, 21, 23, 24, 27, 32, 35, 39, 41, 45, 47, 52, 53, 61, 63, 67, 69, 73, 76, 77, 84, 85, 91, 94, 95, 96, 97, and 99.
3193 is palindromic in (at least) the following bases: 29, 42, 56, -57, -76, and -84.
3193 in base 7 = 12211 and consists of only the digits '1' and '2'.
3193 in base 29 = 3n3 and consists of only the digits '3' and 'n'.
3193 in base 32 = 33p and consists of only the digits '3' and 'p'.
3193 in base 41 = 1aa and consists of only the digits '1' and 'a'.
3193 in base 42 = 1Y1 and consists of only the digits '1' and 'Y'.
3193 in base 55 = 133 and consists of only the digits '1' and '3'.
3193 in base 56 = 111 and consists of only the digit '1'.

The number 3193 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001595: a(n) = a(n-1) + a(n-2) + 1, with a(0) = a(1) = 1.
A054569: a(n) = 4*n^2 - 6*n + 3.
A062114: a(n) = 2*Fibonacci(n) - (1 - (-1)^n)/2.
A062668: Composite and every divisor (except 1) contains the digit 3.
A066983: a(n+2) = a(n+1) + a(n) + (-1)^n, with a(1) = a(2) = 1.
A099971: Write (sqrt(5)-1)/2 as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.
A144781: Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 8.
A161532: a(n) = 2n^2 + 8n + 1.
A277699: Main diagonal of A277320: a(n) = A048720(n, A065621(n)).
A325534: Number of separable partitions of n; see Comments.