Number of the day: 6787

Srinivasa Ramanujan was born on this day 133 years ago.

Properties of the number 6787:

6787 = 11 × 617 is semiprime and squarefree.
6787 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 6160 totatives.
6787 has a triangular digit sum 28 in base 10.
6787 has an oblong digit product 2352 in base 10.
6787 = 3394² - 3393² = 314² - 303² is the difference of 2 nonnegative squares in 2 ways.
6787 is the sum of 2 positive triangular numbers.
6787 is the difference of 2 positive pentagonal numbers in 2 ways.
6787 = 1² + 15² + 81² is the sum of 3 positive squares.
6787² = 1155² + 6688² is the sum of 2 positive squares in 1 way.
6787² is the sum of 3 positive squares.
6787 is a proper divisor of 1409¹¹ - 1.
6787 is an emirpimes in (at least) the following bases: 2, 3, 14, 18, 23, 24, 25, 34, 39, 41, 44, 47, 52, 55, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 81, 89, 91, 92, 94, 95, 96, 98, 99, and 100.
6787 is palindromic in (at least) the following bases: 30, 78, -27, -53, -59, and -87.
6787 in base 26 = a11 and consists of only the digits '1' and 'a'.
6787 in base 30 = 7g7 and consists of only the digits '7' and 'g'.
6787 in base 47 = 33J and consists of only the digits '3' and 'J'.
6787 in base 58 = 211 and consists of only the digits '1' and '2'.

The number 6787 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005674: a(n) = 2^(n-1) + 2^[ n/2 ] + 2^[ (n-1)/2 ] - F(n+3).
A062020: Let P(n) = { 2,3,5,7,...,p(n) } where p(n) is n-th prime; then a(1) =0 and a(n) = Sum [mod{p(i) - p(j)}], for all i and j from 1 to n.
A072481: a(n) = Sum_{k=1..n} Sum_{d=1..k} (k mod d).
A080855: a(n) = (9*n^2 - 3*n + 2)/2.
A082395: Number of shifted Young tableaux with height <= 3.
A107632: Subsequence of A107629. Consider a Gaussian prime a+bi with index k in A103431. k is in A107632 when an integer multiplier m exists such that the distance of m*norm(a+bi) to k is minimal up to k. abs(m*norm(a+bi) - k) is minimal up to k. A107633 gives the squares of the norms of these Gaussian primes, A107634 the integer multipliers m.
A135602: Right-angled numbers with an internal digit as the vertex.
A188135: a(n) = 8*n^2 + 2*n + 1.
A217030: Semiprimes p such that next semiprime after p is p + 10.
A241819: Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >=... >= x(k), of n such that max(x(i) - x(i-1)) <= number of distinct parts of p.