4th of June Crossnumber

1234567891011121314
Across
  1. 1. the first three digits of pi when written in base 8
  2. 3. the ultimate answer to life, the universe, and everything
  3. 5. 12th Fibonacci number (the first two being 1 and 1) divided by the 12th square number plus the 12th triangle number = A
  4. 7. a Mersenne prime = B
  5. 9. the number of 8-digit palindromic numbers plus the cardinality of the power set of {1,2,3,4,5,7,8,9,10}
  6. 10. has exactly 3 factors
  7. 11. [e^2+e+1]!
  8. 13. Z^4+2Z, where Z = 5cos(arctan(4/3))
  9. 14. B - A^2
Down
  1. 1. 44 x 33 x 22 x 11
  2. 2. a taxicab number
  3. 4. the number of unique anagrams of the word 'Etonian'
  4. 6. the sum of two different fifth powers
  5. 7. the sum of all positive factors less than this number
  6. 8. a seventh power = D
  7. 9. C + D
  8. 12. the sum of the solutions to the equation: '11x^5-135795x^4+22x^3-19x^2+1447890x-7 = 0' = C