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46 Forty-Six XLVI i i iii i i iiiii i i i iiiiiii i i i i iiiiiiiii i i i i i i i i i i i Corresponding ordinal: forty-sixth. The number 46 is the twenty-fourth even number and the thirty-first composite number. The number 46 is a centered triangular number, as you can see. As a product of primes: 46 = 2 23. The number 46 has four divisors: 1, 2, 23, 46. The number 46 is the thirty-sixth deficient number: s(36) = 1 + 2 + 23 = 26 < 46. As a sum of four or fewer squares: 46 = 12 + 32 + 62 = 12 + 22 + 42 + 52 . As a sum of nine or fewer cubes: 46 = 3 13 + 2 23 + 33 . As a sum of two odd primes: 3 + 43, 5 + 41, 17 + 29, 23 + 23. The number 46 appears in only one Pythagorean triple, [46; 528; 530], which is not primitive because 46 is twice an odd number. The number 46 is the largest even number that is not a sum of two abundant numbers. In fact, every even number greater than 46 is equal to 12, 20, or 40 plus a proper multiple of 6. A (zeroless, restricted) pandigital fraction is one which uses each of the nonzero digits exactly once, like 3187=25496, which is equal to 1=8. There are 46 pandigital fractions equal to 1=8. At age 46, Ulysses Simpson Grant was inaugurated as President of the United States. At age 46, Bill Clinton was inaugurated as President of the United States. At age 46, President John F. Kennedy was assassinated. The forty-sixth state to enter the Union was Oklahoma. 2 Chapter 46 Forty-Six XLVI The forty-sixth largest state in the United States is New Jersey. There are 46 chromosomes in a human cell. The longest year was 46 BC which consisted of 445 days. In that year, Julius Caesar introduced what is now known as the Julian calendar. The extra days were added to make the months conform with the seasons. The 46th word in the King James Version of Psalm 46 is “shake”. The 46th word from the end is “spear”. In the year 1610, when the King James Version came out, William Shakespeare celebrated his 46th birthday.