Number of the day: 3667

Paul Erös was born on this day 106 years ago.

Properties of the number 3667:

3667 is a cyclic number.
3667 = 19 × 193 is semiprime and squarefree.
3667 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 3456 totatives.
3667 has a semiprime digit sum 22 in base 10.
3667 has an oblong digit product 756 in base 10.
Reversing the decimal digits of 3667 results in an emirpimes.
3667 = 1834² - 1833² = 106² - 87² is the difference of 2 nonnegative squares in 2 ways.
3667 is the sum of 2 positive triangular numbers.
3667 is the difference of 2 positive pentagonal numbers in 2 ways.
3667 = 11² + 39² + 45² is the sum of 3 positive squares.
3667² = 1805² + 3192² is the sum of 2 positive squares in 1 way.
3667² is the sum of 3 positive squares.
3667 is a proper divisor of 277³ - 1.
3667 is an emirpimes in (at least) the following bases: 2, 3, 5, 6, 8, 10, 11, 16, 18, 20, 22, 27, 29, 31, 32, 34, 36, 37, 39, 40, 41, 43, 51, 53, 54, 55, 56, 64, 66, 67, 70, 71, 72, 77, 79, 82, 89, 91, 94, and 98.
3667 is palindromic in (at least) the following bases: 17, 47, -33, -78, and -94.
3667 in base 17 = cbc and consists of only the digits 'b' and 'c'.
3667 in base 46 = 1XX and consists of only the digits '1' and 'X'.
3667 in base 47 = 1V1 and consists of only the digits '1' and 'V'.
3667 in base 60 = 117 and consists of only the digits '1' and '7'.

The number 3667 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007442: Inverse binomial transform of primes.
A078414: a(n) = (a(n-1)+a(n-2))/7^k, where 7^k is the highest power of 7 dividing a(n-1)+a(n-2).
A087886: Numbers n such that 29^n + 2 is prime.
A088405: a(n) = A052217(n)/3.
A114736: Number of planar partitions of n where parts strictly decrease along each row and column.
A147875: Second heptagonal numbers: a(n) = n*(5*n+3)/2.
A227523: Values of n such that L(20) and N(20) 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.
A237424: Numbers of the form (10^a + 10^b + 1)/3.
A264351: The x member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for odd D(n) = A263012(n).
A303084: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.