Monday, July 20, 2009

1634

1634 = 2 x 19 x 43.

1634 is the smallest number (except 1) that is the sum of the fourth powers of its digits: 1634 = 14 + 64+ 34 + 44. The other four-digit numbers that are the sums of the fourth powers of their digits are 8208 and 9474. A number that is the sum of the nth powers of its digits is called a narcissistic number.

1634 and 1635 have the same sum of divisors: 1 + 2 + 19 + 38 + 43 + 86 + 817 + 1634 = 1 + 3 + 5 + 15 + 109 + 327 + 545 + 1635. They also both have the same number of divisors.

1634, 1635, and 1636 are each the product of exactly three primes.

In base 5, 1634 has five distinct digits: 23014.


In the year
1634, the first settlers arrived in St. Mary's City, Md., to form the fourth permanent settlement in British North America.

Source:
The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.
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