Thursday, August 25, 2016

Number of the day: 34384

Properties of the number 34384:

34384 = 24 × 7 × 307 is the 30708th composite number and is not squarefree.
34384 has 3 distinct prime factors, 20 divisors, 13 antidivisors and 14688 totatives.
34384 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 34384 results in a semiprime.
34384 = 85972 - 85952 = 43002 - 42962 = 21532 - 21452 = 12352 - 12212 = 6282 - 6002 = 3352 - 2792 is the difference of 2 nonnegative squares in 6 ways.
34384 is the sum of 2 positive triangular numbers.
34384 is the difference of 2 positive pentagonal numbers in 2 ways.
34384 = 722 + 922 + 1442 is the sum of 3 positive squares.
343842 is the sum of 3 positive squares.
34384 is a divisor of 176 - 1.
34384 is palindromic in (at least) the following bases: 33, 52, and 90.
34384 in base 33 = viv and consists of only the digits 'i' and 'v'.
34384 in base 52 = CbC and consists of only the digits 'C' and 'b'.
34384 in base 53 = CCe and consists of only the digits 'C' and 'e'.

The number 34384 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057546: Number of Catalan objects of size n fixed by Catalan Automorphism A057511/A057512 (deep rotation of general parenthesizations/plane trees).
A059376: Jordan function J_3(n).
A063453: Multiplicative with a(p^e) = 1 - p^3.
A082261: Row sums in A082259.
A192349: Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
A211689: Number of -4..4 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two or three distinct values for every i<=n and j<=n

No comments:

Post a Comment