Tuesday, December 20, 2016

Number of the day: 3026

Properties of the number 3026:

3026 = 2 × 17 × 89 is a sphenic number and squarefree.
3026 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 1408 totatives.
3026 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 3026 results in a prime.
3026 = 102 + … + 212 is the sum of at least 2 consecutive positive squares in 1 way.
3026 is the sum of 2 positive triangular numbers.
3026 is the difference of 2 positive pentagonal numbers in 1 way.
3026 = 252 + 492 = 12 + 552 is the sum of 2 positive squares in 2 ways.
3026 = 192 + 362 + 372 is the sum of 3 positive squares.
30262 = 14242 + 26702 = 1102 + 30242 = 17762 + 24502 = 13262 + 27202 is the sum of 2 positive squares in 4 ways.
30262 is the sum of 3 positive squares.
3026 is a divisor of 11234 - 1.
3026 = '302' + '6' is the concatenation of 2 semiprime numbers.
3026 is palindromic in (at least) the following bases: 36, 55, 88, -42, -48, -54, and -55.
3026 in base 6 = 22002 and consists of only the digits '0' and '2'.
3026 in base 27 = 442 and consists of only the digits '2' and '4'.
3026 in base 35 = 2gg and consists of only the digits '2' and 'g'.
3026 in base 36 = 2c2 and consists of only the digits '2' and 'c'.
3026 in base 54 = 122 and consists of only the digits '1' and '2'.
3026 in base 55 = 101 and consists of only the digits '0' and '1'.

The number 3026 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003336: Numbers that are the sum of 2 nonzero 4th powers.
A035959: Number of partitions of n in which no parts are multiples of 5.
A059929: a(n) = Fibonacci(n)*Fibonacci(n+2).
A069894: Centered square numbers: 4*n^2 + 4*n + 2.
A070550: a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3.
A075205: Number of polyominoes with n cells that tile the plane isohedrally.
A092229: Numbers n such that numerator of Bernoulli(2n) is divisible by 257, the tenth irregular prime.
A133535: Sum of fourth powers of two consecutive primes.
A134406: Composite numbers of the form n^2 + 1.
A264272: T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

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