Sunday, March 4, 2018

Number of the day: 789

Properties of the number 789:

789 is a cyclic number.
789 = 3 × 263 is semiprime and squarefree.
789 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 524 totatives.
789 has sum of divisors equal to 1056 which is an oblong number.
Reversing the decimal digits of 789 results in a sphenic number.
Reversing the decimal digits of 789 results in a Fibonacci number.
789 = 52 + … + 132 is the sum of at least 2 consecutive positive squares in 1 way.
789 = 3952 - 3942 = 1332 - 1302 is the difference of 2 nonnegative squares in 2 ways.
789 is the difference of 2 positive pentagonal numbers in 1 way.
789 = 12 + 22 + 282 is the sum of 3 positive squares.
7892 is the sum of 3 positive squares.
789 is a proper divisor of 10512 - 1.
789 = '7' + '89' is the concatenation of 2 prime numbers.
789 is an emirpimes in (at least) the following bases: 4, 6, 7, 8, 16, 17, 19, 20, 21, 23, 26, 27, 28, 29, 35, 39, 44, 46, 55, 60, 61, 65, 66, 71, 73, 75, 77, 85, 86, 89, 90, 93, and 100.
789 in base 6 = 3353 and consists of only the digits '3' and '5'.
789 in base 12 = 559 and consists of only the digits '5' and '9'.

The number 789 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024199: a(n) = (2n-1)!! * Sum_{k=0..n-1}(-1)^k/(2k+1).
A025328: Numbers that are the sum of 3 nonzero squares in exactly 8 ways.
A025335: Numbers that are the sum of 3 nonzero squares in 7 or more ways.
A033075: Positive numbers n such that all pairs of consecutive decimal digits differ by 1.
A069606: a(1) = 4; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.
A071148: Partial sums of sequence of odd primes (A065091); a(n) = sum of the first n odd primes.
A091214: Composite numbers whose binary representation encodes a polynomial irreducible over GF(2).
A147562: Number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton.
A186651: Total number of positive integers below 10^n requiring 3 positive biquadrates in their representation as sum of biquadrates.
A299285: Coordination sequence for "tea" 3D uniform tiling.

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