Thursday, June 8, 2017

Number of the day: 21414

Properties of the number 21414:

21414 = 2 × 3 × 43 × 83 is the 19009th composite number and is squarefree.
21414 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 6888 totatives.
21414 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 21414 results in an oblong number.
21414 is the difference of 2 positive pentagonal numbers in 2 ways.
21414 = 102 + 172 + 1452 is the sum of 3 positive squares.
214142 is the sum of 3 positive squares.
21414 is a proper divisor of 13276 - 1.
21414 = '214' + '14' is the concatenation of 2 semiprime numbers.
21414 is palindromic in (at least) the following bases: 41, -30, and -40.
21414 in base 9 = 32333 and consists of only the digits '2' and '3'.
21414 in base 13 = 9993 and consists of only the digits '3' and '9'.
21414 in base 30 = nno and consists of only the digits 'n' and 'o'.
21414 in base 39 = E33 and consists of only the digits '3' and 'E'.
21414 in base 41 = CUC and consists of only the digits 'C' and 'U'.

The number 21414 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032240: Number of identity bracelets of n beads of 3 colors.
A043468: Numbers n such that number of 3's in base 9 is 4.
A074303: Sum of squares of digits of n is equal to the largest prime factor of n reversed, where the largest prime factor is not a palindrome.
A167690: The even composites n such that n=q*g*j*y and q+g=j*y where q,g,j,y are primes.
A200075: G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1 + x^2*A(x)^3).
A211850: Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1
A260761: Number of (n+2)X(2+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010011
A283003: Intersection of A003052 and A283002.

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